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In this short paper we present a necessary and sufficient condition for that the one‐dimensional mass transport equation has one unique L1 weak solution.

In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.In this paper, we solve the fractional Bagley-Torvik equation by using discrete cubic spline and a fourth order approxi-mation based on weighted shifted Grunwald-Letnikov difference operator. By matrix analysis, the numerical scheme is proved to be uniquely solvable and third order accurate. An example is presented to verify the efficiency of the numerical scheme and to compare with other methods in the literature.

The paper considers the influence of the assumed error indicator on the final adapted mesh. Provided that threshold values of an error are increased by applying the adaptive procedure, it turns out that final mesh depends on the assumed error indicator. In the paper, there were used the standard error estimates and the error indicator proposed by the author. The proposed error indicator is based on applying hierarchically generalized finite difference method (FDM). In the case of the proposed error indicator, the final adapted mesh is the most optimal for the exact solution.

This paper presents the calculation of the gas flow through the piston ring pack of the combustion engine. The paper compares the solution of ordinary differential equations using the standard numerical methods (ode solvers present in MATLAB) with a new method based on the Taylor series – Modern Taylor Series Method.This paper presents the calculation of the gas flow through the piston ring pack of the combustion engine. The paper compares the solution of ordinary differential equations using the standard numerical methods (ode solvers present in MATLAB) with a new method based on the Taylor series – Modern Taylor Series Method.

This paper reports a new numerical method based on Bernoulli polynomials for the solution of Helmholtz equations. The method uses matrix forms of Bernoulli polynomials and their derivatives by means of collocation points. Aim of this paper is to solve Helmholtz equations using this matrix relations. © 2017 Author(s).

The aim of this paper is to develop numerical methods for solving systems of integral equations with cardinal splines. The unknown functions are expressed as a linear combination of horizontal translations of certain cardinal spline functions with small compact supports. Then a simple system of equations on the coefficients is obtained for the system of integral equations. It is relatively straight forward to solve the system of unknowns and an approximation of the original solution with high accuracy is achieved. Several cardinal splines are used in the paper to enhance the accuracy. The sufficient condition for the existence of the inverse matrix is examined and the convergence rate is investigated. Examples are given to demonstrate the benefits of the methods.

The main focus of the paper is the analysis of the influence of residual stress on the ultimate limit state of a hot‐rolled member in compression. The member was modelled using thin‐walled elements of type SHELL 181 and meshed in the programme ANSYS. Geometrical and material non‐linear analysis was used. The influence of residual stress was studied using variance‐based sensitivity analysis. In order to obtain more general results, the non‐dimensional slenderness was selected as a study parameter. Comparison of the influence of the residual stress with the influence of other dominant imperfections is illustrated in the conclusion of the paper. All input random variables were considered according to results of experimental research.

This paper presents the boundary element method (BEM) algorithm for the 2D steady‐state heat conduction problem of particulate composite in which a thermal boundary resistance exists at constituent interfaces. The numerical implementation of the boundary integral equations is based on linear elements after boundary discretization. BEM formulation which incorporates the imperfect interface effects is developed for steady 2D simulations of the temperature distributions of composites containing randomly distributed particles of different sizes. The randomly distributed particles investigated in this paper include circular particles and square particles with different orientations. The temperature distributions of steady‐state conduction inside the composite are simulated using the present BEM formulation. Numerical examples for composite with different particle geometries are presented, which illustrate the accuracy, suitability and efficiency of the present BEM algorithm for the approximations of steady‐state heat conduction under either perfect or imperfect interfacial thermal contact conditions. The main advantage of BEM compared with the conventional methods is that it significantly reduces the dimensionality of the problem, resulting in a comparatively smaller system of equations to be solved. Compared to available solutions obtained by other numerical method, it provides an efficient and powerful analytical tool for steady‐state solutions of constituents, such as particles with thermal barrier resistance across interfaces.

This paper presents a modified Thiele‐Werner algorithm to construct a kind of reliable vector‐valued rational interpolants (RVRIs) and then studies their existence. The reliability of this method means that if a solution of the basic vector‐valued rational interpolation problem exists, the method given in this paper finds it. Then a method for testing the existence for RVRIs and some methods for dealing with unattainable points for RVRIs are given.

The paper gives Lyapunov type sufficient conditions for partial finite‐time and asymptotic stability in which some state variables converge to zero while the rest converge to constant values that possibly depend on the initial conditions. The paper then presents partially asymptotically stabilizing controllers for many nonlinear control systems for which continuous asymptotically stabilizing (in the usual sense) controllers are known not to exist.

In the paper we consider quasi‐cyclic hyper‐complex variables which are naturally related to the partial differential equations with complex variables. In fact, we develop a matrix 4×4 generalization of the classical bicomplex numbers [1], [2]. We recall that a matrix 2×2 isomorphic type treatment of the classical bicomplex numbers was developed in [3]. Here we develop a matrix 4×4 generalization of the bicomplex numbers including some improvement of the papers [3] and [4]. Let us remark that a deep generalization of the considered ideas was sketch in [5] before us.

This paper shows the existence of nonautonomous projected dynamical systems in Hilbert spaces. These systems arise most recently in the work being done on evolutionary variational inequalities (EVI) and help in extending the mix between the dynamics given by EVI and the disequilibrium evolution of equilibrium problems. This paper fills a gap in the current study of dynamic evolution of equilibrium problems.

This paper deals with the construction of numerical methods of random initial value problems. Random linear multistep methods are presented and sufficient conditions for their mean square convergence are established. Main statistical properties of the approximations processes are computed in several illustrative examples. Copyright © 2010 John Wiley & Sons, Ltd., Thanks to the anonymous reviewer whose comments greatly enhanced the paper. This work has been partially supported by the Spanish M.E.C. and FEDER grants MTM2009-08587 and TRA2007-68006-C02-02, the Universidad Politecnica de Valencia grant PAID-06-09 (ref. 2588) and Mexican Conacyt.

In the recent papers [8], [2], and [9] three numerical methods preserving some properties of the analytical solution of a linear stochastic oscillator have been proposed. In this paper we study further properties of these schemes and confirm experimentally the conclusions.

Nonparametric Bayesian approaches to density estimation (“Bayesian field theories”) have typically to be solved numerically on a lattice. This is often numerically quite expensive. The Paper wants to show that such numerical calculations are nowadays feasible for some interesting problem classes. In particular, Bayesian field theories are defined by 1. a likelihood model, being a probabilistic description of the measurement process of observational data. and 2. a prior model, determining the generalization behavior of the theory by implementing available a priori knowledge. In this Paper some variations of prior and likelihood models are discussed: First, the implementation of approximate symmetries with Gaussian process priors is demonstrated for approximate periodic and for approximate fractal functions. Second, besides a discussion of the classical likelihood models of general density estimation and regression, special emphasis is put on the likelihood model of quantum theory to treat the inverse probl...

The paper describes numerical methods of search engine optimization of combinations of alphabets of random variables and the search for optimal modes of complex processes with the formation of optimal subsets trees. A method for solving discrete optimization problems using optimal subsets of random variables of various degrees of detail is considered. The combinations of alphabets are adjusted at the subsequent stages of the process, depending on the dynamics of its flow at the previous stages with the help of the optimal set tree of complex shape.

In this paper, the effects of water on obstacles in the dam break flow problem are investigated numerically. The numerical method is based on the Navier-Stokes equations describing the flow of an incompressible viscous fluid and the equation for the phase. As a numerical method for solving equations, the numerical algorithm PISO was chosen. The water surface movement is captured by using the volume of fluid (VOF) method, which leads to a strict mass conservation. Moreover the accuracy and reliability of the 3D model were tested using large-scale laboratory experiments on dam destruction problem. The obtained free surface dynamics was compared with the experimental data and numerical results of other authors. These numerical results gave good agreement with the experimental data. By dam break flow problem simulation, the best turbulent models were chosen, which describe almost the same pressure distribution as in the experiment. Finally, various forms of obstacles were examined, by which the pressure distributions were reduced three times on the dam surface.

The Nystrom-Clenshaw-Curtis (NCC) quadrature, which was proposed in [S. Y. Kang, I. Koltracht, and G. Rawitscher, Math. Comp. 72, 729–756 (2003)], is a highly accurate numerical method for solving integral equations with semi-smooth kernel. In this paper, we introduce the basic idea of the NCC quadrature and derive an NCC quadrature for Volterra integral equations with proportional delays. Numerical results are presented to illustrated the high accuracy of the method.

The numerical method to solve multimaterial topology optimization problems for elastic bodies in unilateral contact with Tresca friction is developed in the paper. The displacement of the elastic body in contact is governed by elliptic equation with inequality boundary conditions. The body is assumed to consists from more than two distinct isotropic elastic materials. The materials distribution function is chosen as the design variable. Since high contact stress appears during the contact phenomenon the aim of the structural optimization problem is to find such topology of the domain occupied by the body that the normal contact stress along the boundary of the body is minimized. The original cost functional is regularized using the multiphase volume constrained Ginzburg-Landau energy functional rather than the perimeter functional. The first order necessary optimality condition is recalled and used to formulate the generalized gradient flow equations of Allen–Cahn type. The optimal topology is obtained as...

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki, GREECE, WOS: 000445105400302, In this paper, we give a generalization of absolutely almost convergence, and prove interesting results.

International Conference of Numerical Analysis and Applied Mathematics (ICNAAM) -- SEP 25-30, 2017 -- Thessaloniki, GREECE, WOS: 000445105400303, In this paper, the concept of a strongly lacunary delta(2) quasi-Cauchy sequence is introduced. We proved interesting theorems related to strongly lacunary delta(2) -quasi-Cauchy sequences. A real valued function f defined on a subset A of the set of real numbers, is strongly lacunary delta(2) ward continuous on A if it preserves strongly lacunary delta(2) quasi-Cauchy sequences of points in A, i.e. (f(alpha(k))) is a strongly lacunary delta(2) quasi-Cauchy sequence whenever (alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequences of points in A, where a sequence (alpha(k)) is called strongly lacunary delta(2) quasi-Cauchy if (Delta(2)alpha(k)) is a strongly lacunary delta(2) quasi-Cauchy sequence where Delta(2)alpha(k) = alpha(k+2)-2 alpha(k+1)+ alpha(k) for each positive integer k.

In this paper the analysis of the fuel optimal control of the plane oscillations of the satellite on the circular orbit subject to the aerodynamic moment variations has been done. On basis of necessary conditions of optimality the problem was reduced to the task of nonlinear programming. The numerical method of the sequential linearization of the boundary conditions for calculation of the switching moments has been proposed and its implementation has been presented. Examples for the different areas of the initial states have been calculated.

In this paper we study the fourth order Boussinesq equation with a single nonlinearity. We rewrite this equation in a Hamiltonian form and present a noncompact finite difference scheme, which preserves the symplectic structure of the initial problem. We construct a new finite difference scheme, which is very similar to the symplectic scheme but preserves the discrete energy exactly. To illustrate both schemes we present many computational results. We compare the performance of the symplectic scheme with the new conservative finite difference scheme.

In this paper we present a new numerical method for solving fractional differential equations (FDEs) based on Genocchi polynomials operational matrix through collocation method. The operational matrix of fractional integration in Riemann-Liouville sense is derived. The upper bound for the error of the operational matrix of fractional integration is also shown. The properties of Genocchi polynomials are utilized to reduce the given problems to a system of algebraic equations. Illustrative examples are finally given to show the simplicity, accuracy and applicability of the method.

In this paper, we reformulate the Vlasov-Maxwell equations based on the Morrison-Marsden-Weinstein Poisson bracket. In order to get the numerical solutions preserving the Poisson bracket, we split the Hamiltonian of the Vlasov-Maxwell equations into five parts. We construct the numerical methods for the time direction via composing the exact solutions of subsystems. By combining an appropriate spatial discretization, we can prove that the resulting numerical discretization preserves the discrete Poisson bracket. We present numerical simulations for the problems of Landau damping and two-stream stability.

The present paper is concerned with the numerical modeling of magneto-acoustic Wave Phase Conjugation (WPC) phenomena. Since ultrasonic waves in the WPC applications have short wavelengths relative to the traveling distances, high-order numerical methods in both space and time domains are required. The numerical scheme chosen for the current research is the Runge-Kutta Discontinuous Galerkin (RKDG) method incorporated into the Correction Procedure via Reconstruction (CPR) framework. In order to avoid non-physical oscillations near high-gradient regions, a Weighted Essentially Non-Oscillatory (WENO) limiter is used to reconstruct the solutions in the affected cells. After being assured that the numerical scheme has appropriate accuracy and performance, the WPC process is modeled in both linear and non-linear regimes. The results in the linear regime are in acceptable agreement with the analytical solution. The only significant deviation between the linear and non-linear results is at the sensor within the ...

In the proposed paper we continue the study of the diaphony, defined in b-adic number system, and we extend it in different directions. We investigate this diaphony as a tool for estimation of the pseudorandom properties of some of the most used random number generators. This is done by evaluating the distribution of specially constructed two-dimensional nets on the base of the obtained random numbers. The aim is to see how the generated numbers are suitable for calculations in some numerical methods (Monte Carlo etc.).

In this paper, we simulate some of the benchmark problems proposed by the World Federation of Nondestructive Evaluation Centers (WFNDEC) using a full wave simulation model based on accurate solutions to the boundary integral equations for ultrasonic scattering. Much of the previous work on modeling these problems relied on the Kirch-hoff approximation to find the scattered fields from defects. Here we instead use a numerical method, called the Nystrom method, for finding the scattered fields more accurately by solving the boundary integral equations of scattering. We compare our model’s predictions with both measurements and Kirchhoff approximation based models. We expect the presented results to serve as a validation of our model as well as a comparison between the Kirchhoff approximation and the Nystrom method.

In this paper, a numerical method is proposed to solve the Fredholm-Volterra fractional integro-differential equation with nonlocal boundary conditions by using Haar wavelets. A collocation based Galerkin’s method is applied by using Haar wavelets as basis functions over the interval [0, 1). It converts the Fredholm-Volterra fractional integro-differential equation into a system of m linear equations. On incorporating q nonlocal boundary conditions, it leads to further q equations. All together it will give a system of (m + q) linear equations in (m + q) variables which can be solved. A variety of test examples are considered to illustrate the proposed method. The actual error is also measured with respect to a norm and the results are validated through error bounds.