Search

Meta‐analysis is a widely used tool for synthesizing results from multiple studies. The collected studies are deemed heterogeneous when they do not share a common underlying effect size; thus, the factors attributable to the heterogeneity need to be carefully considered. A critical problem in meta‐analyses and systematic reviews is that outlying studies are frequently included, which can lead to invalid conclusions and affect the robustness of decision‐making. Outliers may be caused by several factors such as study selection criteria, low study quality, small‐study effects, and so on. Although outlier detection is well‐studied in the statistical community, limited attention has been paid to meta‐analysis. The conventional outlier detection method in meta‐analysis is based on a leave‐one‐study‐out procedure. However, when calculating a potentially outlying study's deviation, other outliers could substantially impact its result. This article proposes an iterative method to detect potential outliers, which reduces such an impact that could confound the detection. Furthermore, we adopt bagging to provide valid inference for sensitivity analyses of excluding outliers. Based on simulation studies, the proposed iterative method yields smaller bias and heterogeneity after performing a sensitivity analysis to remove the identified outliers. It also provides higher accuracy on outlier detection. Two case studies are used to illustrate the proposed method's real‐world performance. [ABSTRACT FROM AUTHOR]

The goal of this study is to construct a novel iterative method to compute the matrix sign function using a different approach. It is discussed that the new method is globally convergent and asymptotically stable. It achieves the sixth order of convergence and only requires five matrix–matrix multiplications. The obtained results are extended to compute the number of eigenvalues of a matrix in a specified region of the complex plane. This is done by performing appropriate sequence of matrix sign computations. An application of this technique has been discussed in stability analysis of linear time‐invariant dynamic systems in control theory. Numerical results have been given to justify the effectual performance and superiority of the proposed method. Matrices of various sizes have been considered for this purpose. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]

In this research article, we propose a new matrix iterative method with a convergence order of five for computing the sign of a complex matrix by examining the different patterns and symmetry of existing methods. Analysis of the convergence of the method was explored on a global scale, and attraction basins were demonstrated. In addition to this, the asymptotic stability of the scheme was explored.Then, an algorithm for determing thegeneralized eigenvalues for the case of regular matrix pencils was investigated using the matrix sign computation. We performed a series of numerical experiments using numerous matrices to confirm the usefulness and superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Parameter identification problems in PDEs are special class of nonlinear inverse problems which has many applications in science and technology. One such application is the Electrical Impedance Tomography (EIT) problem. Although many methods are available in literature to tackle nonlinear problems, the computation of Fréchet derivative is often a bottle neck for deriving the solution. Moreover, many assumptions are required to establish the convergence of such methods. In this paper, we propose a modified form of Levenberg–Marquardt scheme which does not require the knowledge of exact Fréchet derivative, instead, uses an approximate form of it and at the same time, no additional assumptions are required to establish the convergence of the scheme. We illustrate the theoretical result through numerical examples. In order to ensure that the proposed scheme can be applied to practical problems, we have applied the scheme to EIT problem and the reconstruction process clearly demonstrates that the method can be successfully applied to practical problems. [ABSTRACT FROM AUTHOR]

In this article, based on the structural properties of the coefficient matrix obtained through the discretization of constrained optimal control problems under the time-harmonic parabolic equation, we propose and compare two types of algorithms, namely the Optimized PU (OPU) method and the optimized double-step (ODS) method. It can be theoretically proven that both of these iterative methods have a convergence rate of 0.1716, which can even be optimized to reach 0.0396. Additionally, we demonstrate that these two methods avoid the common drawback of many methods in terms of parameter selection, where the parameters often depend on the matrix's eigenvalues. The convergence rate of 0.1716 can be easily achieved through a single constant setup in the proposed two methods. Furthermore, we also compare the algorithmic complexity of the OPU method, the ODS method, and the latest RSS-like method in each step of the iterative process, which demonstrates that the OPU method and ODS method exhibit advantages in computational storage or calculation complexity. Finally, to demonstrate the effectiveness of our proposed optimized iterative methods and the validity of our theoretical findings, we conduct numerical experiments. The results provide strong empirical support for the efficiency and reliability of these methods. [ABSTRACT FROM AUTHOR]

This study presents some new iterative algorithms based on the gradient method to solve general constrained systems of conjugate transpose matrix equations for both real and complex matrices. In addition, we analyze the convergence properties of these methods and provide numerical techniques to determine the solutions. The effectiveness of the proposed iterative methods is demonstrated through various numerical examples employed in this study. [ABSTRACT FROM AUTHOR]

In this paper we extend dynamic programming techniques to the study of discrete-time infinite horizon optimal control problems on compact control invariant sets with state-independent best asymptotic average cost. To this end we analyse the interplay of dissipativity and optimal control, and propose novel recursive approaches for the solution of so called shifted Bellman Equations. [ABSTRACT FROM AUTHOR]

The article contains a study of methods for solving integral equations in the context of acoustic problems. The methodology considered is applied to describe acoustic wave propagation and scattering. Efficient discretization methods are used together with iterative methods to solve the operator equations, including an apparatus for fast multiplication of the resulting post-discretization Toeplitz matrices by a vector using the fast Fourier transform. The theoretical analysis of the proposed numerical algorithm demonstrates its efficiency in terms of the required number of arithmetic operations and the memory footprint of the computing system. The presented numerical simulation demonstrates the possibility of solving the problem of acoustic wave propagation in transparent media using the proposed methods. A visualization of the obtained solutions for a practical problem with a high level of discretization of the solution volume domain is also presented. [ABSTRACT FROM AUTHOR]

In this work, first, a family of fourth‐order methods is proposed to solve nonlinear equations. The methods satisfy the Kung‐Traub optimality conjecture. By developing the methods into memory methods, their efficiency indices are increased. Then, the methods are extended to the multi‐step methods for finding the solutions to systems of problems. The formula for the order of convergence of the multi‐step iterative methods is 2p$$ 2p $$, where p$$ p $$ is the step number of the methods. It is clear that computing the Jacobian matrix derivative evaluation and its inversion are expensive; therefore, we compute them only once in every cycle of the methods. The important feature of these multi‐step methods is their high‐efficiency index. Numerical examples that confirm the theoretical results are performed. In applications, some nonlinear problems related to the numerical approximation of fractional differential equations (FDEs) are constructed and solved by the proposed methods. [ABSTRACT FROM AUTHOR]

We have conducted a gravity study using ground gravity data, via an automated iterative forward modelling method, to determine the Moho depth map in parts of the Zagros Mountains. The method used, the Maximum Difference Reduction (MDR) method, consists in a modification of the well-known Bott method for solving nonlinear inverse problems. The main characteristics of the MDR algorithm are: 1) the subsurface is divided into rectangular blocks to determine the gravity effect; 2) the density contrast is defined as a priori information, and is considered constant in the whole body. Therefore, we have no non-uniqueness; 3) depth correction in any station stops when the sign of a residual gravity anomaly differs from that of an observed one. As a result, the algorithm moves in one direction, and convergence occurs; 4) the inversion process stops when the residual anomalies fall within a predefined error range, which is controlled by the chi-square criteria. The method has been examined through a synthetic model and, then, applied to determine the Moho depth under the Zagros Mountains. The maximum Moho depth in the Zagros fold-thrust belt, Sanandaj-Sirjan zone, Urumieh-Dokhtar magmatic arc and central Iran, are found respectively at 45, 68, 52, and 42 km. [ABSTRACT FROM AUTHOR]

Symmetric-type methods (STM) without derivatives have been used extensively to solve nonlinear equations in various spaces. In particular, multi-step STMs of a higher order of convergence are very useful. By freezing the divided differences in the methods and using a weight operator a method is generated using m steps (m a natural number) of convergence order 2 m. This method avoids a large increase in the number of operator evaluations. However, there are several problems with the conditions used to show the convergence: the existence of high order derivatives is assumed, which are not in the method; there are no a priori results for the error distances or information on the uniqueness of the solutions. Therefore, the earlier studies cannot guarantee the convergence of the method to solve nondifferentiable equations. However, the method may converge to the solution. Thus, the convergence conditions can be weakened. These problems arise since the convergence order is determined using the Taylor series which requires the existence of high-order derivatives which are not present in the method, and they may not even exist. These concerns are our motivation for authoring this article. Moreover, the novelty of this article is that all the aforementioned problems are addressed positively, and by using conditions only related to the divided differences in the method. Furthermore, a more challenging and important semi-local analysis of convergence is presented utilizing majorizing sequences in combination with the concept of the generalized continuity of the divided difference involved. The convergence is also extended from the Euclidean to the Banach space. We have chosen to demonstrate our technique in the present method. But it can be used in other studies using the Taylor series to show the convergence of the method. The applicability of other single- or multi-step methods using the inverses of linear operators with or without derivatives can also be extended with the same methodology along the same lines. Several examples are provided to test the theoretical results and validate the performance of the method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a faster iterative method for approximating the fixed points of generalized α -nonexpansive mappings. We prove several weak and strong convergence theorems of the considered method in mild conditions within the control parameters. In order to validate our findings, we present some nontrivial examples of the considered mappings. Furthermore, we show that the class of mappings considered is more general than some nonexpansive-type mappings. Also, we show numerically that the method studied in our article is more efficient than several existing methods. Lastly, we use our main results to approximate the solution of a delay fractional differential equation in the Caputo sense. Our results generalize and improve many well-known existing results. [ABSTRACT FROM AUTHOR]

In this paper, a family of fifth-order Chebyshev–Halley-type iterative methods with one parameter is presented. The convergence order of the new iterative method is analyzed. By obtaining rational operators associated with iterative methods, the stability of the iterative method is studied by using fractal theory. In addition, some strange fixed points and critical points are obtained. By using the parameter space related to the critical points, some parameters with good stability are obtained. The dynamic plane corresponding to these parameters is plotted, visualizing the stability characteristics. Finally, the fractal diagrams of several iterative methods on different polynomials are compared. Both numerical results and fractal graphs show that the new iterative method has good convergence and stability when α = 1 2 . [ABSTRACT FROM AUTHOR]

In this paper, a Newton-type iterative scheme for solving nonlinear systems is designed. In the process of proving the convergence order, we use the higher derivatives of the function and show that the convergence order of this iterative method is six. In order to avoid the influence of the existence of higher derivatives on the proof of convergence, we mainly discuss the convergence of this iterative method under weak conditions. In Banach space, the local convergence of the iterative scheme is established by using the ω -continuity condition of the first-order Fréchet derivative, and the application range of the iterative method is extended. In addition, we also give the radius of a convergence sphere and the uniqueness of its solution. Finally, the superiority of the new iterative method is illustrated by drawing attractive basins and comparing them with the average iterative times of other same-order iterative methods. Additionally, we utilize this iterative method to solve both nonlinear systems and nonlinear matrix sign functions. The applicability of this study is demonstrated by solving practical chemical problems. [ABSTRACT FROM AUTHOR]

We propose an iterative method for solution of a coupled acoustic fluid-solid interaction model. Assuming harmonic excitation in time, we use the pressure-displacement formulation of the acousto-elastic problem. The fluid is assumed to be ideal inviscid compressible medium governed by a wave equation for the acoustic pressure. The linear isotropic elastic structure is described by elastodynamic equations for the displacement field. We impose kinematic and dynamic conditions at the interface: the fluid particles velocity matches the velocity of the solid, and the balance of normal stresses holds. In the proposed iterative method. The fluid and solid subproblems are solved alternatingly, taking into account the interface conditions. The convergence of the iterative algorithm is demonstrated numerically for fluid-solid structures with different periodic, as well as random interfaces. The algorithm is applied for comparison of acoustic properties of fluid-solid structures depending on the geometry of the rough interface. [ABSTRACT FROM AUTHOR]

The present article introduces the notion of marked rhythm and its almost smoothness through a certain transformation Rep, called repulsion map. A marked rhythm consists of a rhythm together with a marker, and the map Rep modifies the marked onset of the rhythm. It is shown that an iteration of the map Rep transforms an arbitrary marked rhythm into an almost smooth one. A numerical criterion for a marked rhythm to be almost smooth is given in terms of the difference of its rhythm part. Smooth rhythms are shown to be always almost smooth, and several examples of almost smooth but not smooth rhythms are constructed. [ABSTRACT FROM AUTHOR]

In this study, our examination centers around the numerical resolution of non-coercive issues using a multi-grid approach. Our particular emphasis is directed towards employing multi-grid methodologies to tackle non-linear variational inequalities. Our primary goal involves confirming the consistent convergence of the multi-grid algorithm. To attain this objective, we make use of fundamental sub-differential calculus and glean insights from the convergence principles of non-linear multi-grid techniques. [ABSTRACT FROM AUTHOR]

A new iterative algorithm is proposed for finding a common solution of an equilibrium problem and a fixed point problem. Then, a strong convergence theorem is proved. As a consequence, they can be obtained some strong convergence theorems for an equilibrium problem and a split common fixed point problem. The obtained theorems can be applied to solve an equilibrium problem and a split common null point problem. The results presented in this paper extend and improve some corresponding ones in the literature. Finally, a numerical example is given to show the validity of the algorithm. [ABSTRACT FROM AUTHOR]

In this work, an improved neutron spectrum unfolding code "Artificial Neural Network Iterative" (ANN_Iter), which utilizes the iterative method combined with artificial neural networks, is proposed for Bonner sphere spectrometer. 201 neutron energy spectra and the corresponding measured responses of Bonner spheres with 15 polyethylene shells of different diameter were provided by an IAEA report. In the process of unfolding, the pre-trained artificial neural network provides a guess spectrum according to the "knowledge" it has learned. The guess spectrum was used as the default initial spectrum in the iterative method, which unfolds the spectrum by the response function and the measured counts. The results show that the ANN_Iter's unfolded spectra have a good agreement with the desired spectra. In addition, their accuracy has improved compared with ANN's guess spectra. [ABSTRACT FROM AUTHOR]

In this work, we carry out the dynamical analysis of a proposed optimal fourth-order iterative family of methods in the complex plane that allows us to find those parametric values for which the corresponding family variant's behavior is stable or unstable. The stability of the class is studied through tools of complex dynamics. Furthermore, we calculate critical and fixed points associated with the rational operator linked to this iterative family. To visualize our findings, we draw dynamical and parameter planes. Hence, we can select the regions where the corresponding method is more efficient or shows chaotic behavior. The conclusions obtained from this stability analysis are used in the numerical section, where the problem of fractional conversion in a chemical reactor and some physical and academic problems are solved. To validate our theoretical findings, we include comparisons with existing methods. [ABSTRACT FROM AUTHOR]

We present and analyze a preconditioned conjugate gradient method (PCG) for solving spatial network problems. Primarily, we consider diffusion and structural mechanics simulations for fiber based materials, but the methodology can be applied to a wide range of models, fulfilling a set of abstract assumptions. The proposed method builds on a classical subspace decomposition into a coarse subspace, realized as the restriction of a finite element space to the nodes of the spatial network, and localized subspaces with support on mesh stars. The main contribution of this work is the convergence analysis of the proposed method. The analysis translates results from finite element theory, including interpolation bounds, to the spatial network setting. A convergence rate of the PCG algorithm, only depending on global bounds of the operator and homogeneity, connectivity and locality constants of the network, is established. The theoretical results are confirmed by several numerical experiments. [ABSTRACT FROM AUTHOR]

We introduce a Tseng extragradient method for solving monotone inclusion problem in Banach space. A strong convergence result of an Halpern inertial extrapolation method for solving the resolvent of sum of two monotone operators without the knowledge of the Lipschitz constant was established. Lastly, we illustrate some numerical behavior of our iterative scheme to showcase the performance of the proposed method compared to other related results in the literature. [ABSTRACT FROM AUTHOR]

A modular string averaging procedure (MSA, for short) for a finite number of operators was first introduced by Reich and Zalas in 2016. The MSA concept provides a flexible algorithmic framework for solving various feasibility problems such as common fixed point and convex feasibility problems. In 2001 Bauschke and Combettes introduced the notion of coherence and applied it to proving weak and strong convergence of many iterative methods. In 2019 Barshad, Reich and Zalas proposed a stronger variant of coherence which provides a more convenient sufficient convergence condition for such methods. In this paper we combine the ideas of both modular string averaging and coherence. Focusing on extending the above MSA procedure to an infinite sequence of operators with admissible controls, we establish strong coherence of its output operators. Various applications of these concepts are presented with respect to weak and strong convergence. They also provide important generalizations of known results, where the weak convergence of sequences of operators generated by the MSA procedure with intermittent controls was considered. [ABSTRACT FROM AUTHOR]

Abstract It is a fact that the problem of multicollinearity adversely effects the estimation of parameters not only in normal linear models but also in generalized linear models (GLMs). In this study, we propose a new estimator by imposing the stochastic restrictions on the parameters and combining the Liu estimator in GLMs to address the problem of multicollinearity. The new estimator is referred to as the stochastic restricted Liu estimator. The novel estimator’s first order approximated form (FOA) is presented to compare it to its competitors using the asymptotic mean square error criterion. Furthermore, two empirical applications using a response variable from the Poisson and Gamma distributions are studied to evaluate the performance of estimators. In addition, a simulation study is conducted by considering a response variable from Binomial distribution for comparisons. Based on simulation study and empirical applications, it is found that the performance of the proposed estimator is better than ML, Liu, and mixed estimators for the appropriate selected biasing parameter. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new fifth-order family of derivative-free iterative methods for solving nonlinear equations. Numerous iterative schemes found in the existing literature either exhibit divergence or fail to work when the function derivative is zero. However, the proposed family of methods successfully works even in such scenarios. We extended this idea to memory-based iterative methods by utilizing self-accelerating parameters derived from the current and previous approximations. As a result, we increased the convergence order from five to ten without requiring additional function evaluations. Analytical proofs of the proposed family of derivative-free methods, both with and without memory, are provided. Furthermore, numerical experimentation on diverse problems reveals the effectiveness and good performance of the proposed methods when compared with well-known existing methods. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the application of an iterative collocation method based on the use of Lagrange polynomials for the numerical solution of a class of nonlinear third-kind Volterra integral equations. The approximate solution is given by explicit formulas. The error analysis of the proposed numerical method is studied theoretically. Some numerical examples are given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

The conjugate gradient (CG) method is a classic Krylov subspace method for solving symmetric positive definite linear systems. We analyze an analogous semi-conjugate gradient (SCG) method, a special case of the existing semi-conjugate direction (SCD) methods, for unsymmetric positive definite linear systems. Unlike CG, SCG requires the solution of a lower triangular linear system to produce each semi-conjugate direction. We prove that SCG is theoretically equivalent to the full orthogonalization method (FOM), which is based on the Arnoldi process and converges in a finite number of steps. Because SCG's triangular system increases in size each iteration, Dai and Yuan [Study on semi-conjugate direction methods for non-symmetric systems, Int. J. Numer. Meth. Eng. 60(8) (2004), pp. 1383–1399] proposed a sliding window implementation (SWI) to improve efficiency. We show that the directions produced are still locally semi-conjugate. A counter-example illustrates that SWI is different from the direct incomplete orthogonalization method (DIOM), which is FOM with a sliding window. Numerical experiments from the convection-diffusion equation and other applications show that SCG is robust and that the sliding window implementation SWI allows SCG to solve large systems efficiently. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the convergence of the Peaceman-Rachford Alternating Direction Implicit method for the system of difference equations, approximating the two-dimensional elliptic equations in rectangular domain with nonlocal integral conditions. The main goal of the paper is the analysis of spectrum structure of difference eigenvalue problem with nonlocal conditions. The convergence of iterative method is proved in the case when the system of eigenvectors is complete. The main results are generalized for the system of difference equations, approximating the differential problem with truncation error O(h4). [ABSTRACT FROM AUTHOR]

Demicontractive operators form an important class of nonexpansive type mappings whose study led researchers to the creation of some beautiful results in the framework of metric fixed-point theory. This article aims to provide an overview of the most relevant results on the approximation of fixed points of single-valued demicontractive mappings in Hilbert spaces. Subsequently, we exhibit the role of additional properties of demicontractive operators, as well as the main features of the employed iterative algorithms to ensure weak convergence or strong convergence. We also include commentaries on the use of demicontractive mappings to solve some important nonlinear problems with the aim of providing a comprehensive starting point to readers who are attempting to apply demicontractive mappings to concrete applications. We conclude with some brief statements on our view on relevant and promising directions of research on demicontractive mappings in nonlinear settings (metric spaces) and some application challenges. [ABSTRACT FROM AUTHOR]

Enriched contraction, a class that contains the Picard -Banach contractions and some nonexpansive mappings, are generalized from Banach space framework into a nonlinear context, namely, geodesic metric spaces of nonpositive curvature. We establish general implications that extend the well-known results for enriched mappings formed on Banach spaces. We also look at the results for fixed points involving the contractions i.e., the limit shadowing property and well-posedness as well as some instances to back up our findings. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze a viscosity implicit midpoint iterative method for a nonexpansive mapping in the framework of CAT(0) space. Further, under the some conditions, strong convergence theorem is proved by the sequence generated by the proposed iterative method, which, also solves the variational inequality problem. Further, the results presented in this paper may be treated as an extension and generalization of some corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

The computation of the sign function of a matrix plays a crucial role in various mathematical applications. It provides a matrix-valued mapping that determines the sign of each eigenvalue of a nonsingular matrix. In this article, we present a novel iterative algorithm designed to efficiently calculate the sign of an invertible matrix, emphasizing the enlargement of attraction basins. The proposed solver exhibits convergence of order four, making it highly efficient for a wide range of matrices. Furthermore, the method demonstrates global convergence properties. We validate the theoretical outcomes through numerical experiments, which confirm the effectiveness and efficiency of our proposed algorithm. [ABSTRACT FROM AUTHOR]

The weight function approach of solving nonlinear equations is presented in this work as a two-step, fourth-order, optimal iterative method. It comes from the idea of the theoretical order of convergence. The performance of the novel method has been assessed on a small number of real-life applications from different domains and contrasted with the fourth-order methods currently in use. Also, we find that this has fewer errors and iterations for the same order than the methods now in use. To examine the dynamical analysis of the proposed method using computer tools, we test some challenging polynomials that explain convergence and other graphical features of the iterative scheme. [ABSTRACT FROM AUTHOR]

Rigorously accounting for mutual coupling effects in antenna array synthesis, generally requires that embedded element patterns (EEPs) be determined. The method of moments (MoM) is typically used. Multiple linear system solutions are required, corresponding to every excitation vector associated with an EEP. This paper presents the direct coupling technique (DCT) to obtain the MoM solution for arrays with disjoint elements, by iteratively solving a series of localized subproblems, one associated with each array element. It utilizes a physics‐based, direct‐coupling approximation to incorporate global coupling into the local problems. Local matrices do not change between iterations or with excitation vectors, hence they can be inverted as a preprocessing step, allowing for efficient solution of multiple excitation configurations. Numerical results demonstrate rapid convergence. The convergence rate can be controlled via local problem domain sizing. Since the DCT is ideally suited to parallelization, it is applicable to very large arrays. [ABSTRACT FROM AUTHOR]

In this work, we discussed the existence and uniqueness of the solution for a fractional boundary value problem involving the Ψ$$ \Psi $$‐Riemann–Liouville operators where we used Banach's fixed point theorem; after that, we applied an iterative method and artificial neural networks technique to solve our main problem. Finally, the approximate solution was plotted. [ABSTRACT FROM AUTHOR]

Initial-boundary value problems for semilinear wave equations with damping term and Neumann boundary conditions on the exterior domain are investigated. In sub-critical and critical cases, blow-up and upper bound lifespan estimates of solutions to the problems which contain power nonlinearity | u | q , derivative nonlinearity | u t | p , combined nonlinearity | u t | p + | u | q , respectively, are derived by applying test function technique and iterative method. The novelty is that lifespan estimates of solutions are associated with the well-known Strauss conjecture and Glassey conjecture. [ABSTRACT FROM AUTHOR]

The paper concerns a new iterative method for approximating a solution of an equilibrium problem involving a monotone and Lipschitz-type bifunction in a Hilbert space. Our method combines the proximal mapping with a regularization technique. When compared with known extragradient methods, the proposed method is seen to have a simpler and more elegant structure. A strong convergence theorem is established under some appropriate conditions imposed on the control parameters. Several experiments are performed in order to illustrate the numerical effectiveness of our new algorithm in comparison with that of existing methods. [ABSTRACT FROM AUTHOR]

In this manuscript, we present a parametric family of derivative‐free three‐step iterative methods with a weight function for solving nonlinear equations. We study various ways of introducing memory to this parametric family in order to increase the order of convergence without new functional evaluations. We also performed numerical experiments to compare the iterative methods from different points of view. [ABSTRACT FROM AUTHOR]

Parameter identification problems in PDEs are special class of nonlinear inverse problems which has many applications in science and technology. One such application is the Electrical Impedance Tomography (EIT) problem. Although many methods are available in literature to tackle nonlinear problems, the computation of Fréchet derivative is often a bottle neck for deriving the solution. Moreover, many assumptions are required to establish the convergence of such methods. In this paper, we propose a modified form of Levenberg–Marquardt scheme which does not require the knowledge of exact Fréchet derivative, instead, uses an approximate form of it and at the same time, no additional assumptions are required to establish the convergence of the scheme. We illustrate the theoretical result through numerical examples. In order to ensure that the proposed scheme can be applied to practical problems, we have applied the scheme to EIT problem and the reconstruction process clearly demonstrates that the method can be successfully applied to practical problems. [ABSTRACT FROM AUTHOR]

The Vehicle Routing Problem (VRP) is a crucial subject in the discipline of logistics and transportation management since it connects the distribution centers to the arrival points of services and goods in the most efficient way possible. Considering the VRP in the framework of operational research, the optimization quality of the VRP mainly depends on an efficient model built for the network and the successful choice for the objective of the model. The optimization problem, which involves the objective function as the ratio of two functions, is described as Fractional Programming (FP), which has attracted noteworthy attention in the previous five decades because of its usefulness in modeling several decision processes in operations research, management science, and economics. In this research, we have studied a Linear Fractional Vehicle Routing Problem (LFVRP) regarding the contribution of the mathematical modeling of VRP to both the optimization literature and the commercial market, which is incontrovertible. For this purpose, we propose an iterative method for LFVRP that aims to optimize the delivery of goods and services while minimizing the rate of total cost/load without any variable transformation technique proposed for the first time. By this methodology of iterative optimization, unlike the literature, the mathematical complexity of the model will be facilitated as a Linear Programming Problem (LPP) and, meanwhile, provide the capability of considering multiple objectives (both cost and load) as one. Furthermore, by this advantage, it has been able to express a green-based approach by presenting an objective that minimizes fuel consumption which constructs transportation expenses, and hence it lowers its carbon footprint for our world while keeping the aim of maximum load. In order to illustrate the effectiveness of our approach, we have built a real-life model with real data in the retail sector in Türkiye and provided a comparative analysis. [ABSTRACT FROM AUTHOR]

In this research, we investigate the numerical solution of second member problems that depend on the solution obtained through a multigrid method. Specifically, we focus on the application of multigrid techniques for solving nonlinear variational inequalities. The main objective is to establish the uniform convergence of the multigrid algorithm. To achieve this, we employ elementary subdifferential calculus and draw insights from the convergence theory of nonlinear multigrid methods. [ABSTRACT FROM AUTHOR]

Nonlinear inverse problems occur in many applications and it can be modelled as an operator equation. Solving such problems is mathematically challenging and interesting due to the fact that in most situations, they are unstable under data perturbations that result in the ill-posedness of the problem. Classical schemes proposed in the literature require many assumptions. Therefore, refinement, as well as the development of efficient schemes for solving these problems, are under continuous development. The steepest descent scheme is one of the standard techniques considered in the literature to solve the nonlinear problem. But this method too requires many assumptions to prove the convergence and convergence rate. In this paper, we propose a modified convergence analysis for the steepest descent scheme with a damped Fréchet derivative and the method requires only weaker and minimal assumptions compared to the standard scheme for establishing the convergence and convergence rate. The theoretical results are illustrated through numerical examples. [ABSTRACT FROM AUTHOR]

In this work, we investigate an iterative method based on viscosity approximation method to approximate a common solution of split monotone variational inclusion problem and fixed point problem for a nonexpansive mapping in the frame work of real Hilbert spaces. Further, strong convergence theorem is proved by the sequences generated by the proposed iterative method under some mild conditions, which is the unique solution of the variational inequality problem. Furthermore, we provide some numerical experiments to support our main result. The results and method presented in this work may be treated as an improvement, extension and refinement of some corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this work we focus on the convex feasibility problem (CFP) in Hilbert space. A specific method in this area that has gained a lot of interest in recent years is the Douglas-Rachford (DR) algorithm. This algorithm was originally introduced in 1956 for solving stationary and non-stationary heat equations. Then in 1979, Lions and Mercier adjusted and extended the algorithm with the aim of solving CFPs and even more general problems, such as finding zeros of the sum of two maximally monotone operators. Many developments which implement various concepts concerning this algorithm have occurred during the last decade. We introduce an unrestricted DR algorithm, which provides a general framework for such concepts. Using unrestricted products of a finite number of strongly nonexpansive operators, we apply this framework to provide new iterative methods, where, inter alia, such operators may be interlaced between the operators used in the scheme of our unrestricted DR algorithm. [ABSTRACT FROM AUTHOR]

Abstract The additional deformation of slab track structure subject to arbitrary soil deformation, and subsequently the dynamic deformation coordination between the track and the soil due to a moving vehicle are of significant importance in the analysis of vehicle-track-soil (VTS) interactions. In this work, the finite element modeling and numerical iterative method are presented to compile a simulation program to reveal the deformation coordinated process of slab track-soil interaction reasonably, where the contact-separation relationship at the slab track-soil interface, the interlayered gap between slab track and soil surface, and additional track deformation are derived as additional geometric excitations of VTS interaction system. In numerical studies, different slab track types considering the unit and the longitudinal connected base plates are taken as illustrative and comparative examples, where the deformation coordinated mechanism of slab track-soil interaction and its influence on vehicle-induced vibrations are clarified. [ABSTRACT FROM AUTHOR]

In this paper, steady-state operating conditions of a doubly fed induction generator (DFIG) are computed considering losses of grid-side (GS) filter. Two different cases are studied for steady-state initialization of the DFIG-based wind turbine systems (WTS). In the first case, active power (P) and reactive power (Q) at DFIG terminals are assumed to be known. In the other case wind speed ( V w ), Q is assumed to be known. Apart from considering losses of the DFIG and GS filter, both the cases also consider the non-unity power factor operation of the grid side converter (GSC). For the first case, steady-state operating conditions are calculated by iterative method as well as by non-iterative method. For the second case, iterative method is used to calculate steady-state operating conditions. Calculation of steady-state values of other subsystems of DFIG-based WTS like drive train, controller and network is also shown. The initial values calculated are validated and compared by performing modal analysis and time-domain simulations. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of quasilinear elliptic equations with gradient terms which arise in several applications in the theory of Heidelberg Ferromagnetism and Magnus, Hydrodynamics, and the Condensed Matter Theory. By performing a change of variables, the original problem is transformed into an equivalent semilinear one. The semilinear equation is solved by applying an iterative method, based on the Mountain Pass Theorem, which allows to solve the original problem. [ABSTRACT FROM AUTHOR]

The global positioning system (GPS) is a satellite navigation system that determines locations. Whenever the baseline satellites are serviced or deactivated, the Space Force often flies more than 24 GPS satellites to maintain coverage. The additional satellites are not regarded as a part of the core constellation but may improve the performance of the GPS. In this study of GPS models, we solved various problems. We examined each set of four satellites separately. Advancements in computer softwares have made computations much more precise. We can use iterative methods to solve GPS problems. Iterative schemes for solving nonlinear equations have always been of great importance because of their applicability to real-world problems. This paper involves the development of an efficient family of sixth-order Jarratt-type iterative schemes for analyzing nonlinear global positioning systems. [ABSTRACT FROM AUTHOR]