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The constancy of the power system maintains equilibrium in normal conditions. If the system is subjected to disturbance, it must return to a stable state. Depending on the components and operating conditions of the network, the instability takes many forms. A resistance was added to the faulty bus, and for the purpose of reinforcement, its value was increased. Still, a decrease in the angle value was observed, and this situation is considered undesirable. Therefore, the braking elements technique was used for the purpose of improving the transient stability of the system. The elements were mathematically represented and modeled for the purposes of transient constancy calculations using Euler's developed iterative method for numerical integration. The time has been increased without adding other operations to improve stability and obtain the critical clearance time. One system, which consists of five generalities, including two for obstetrics, was selected for the purpose of conducting the study. The results confirmed the effectiveness of this method in improving the network stability of the system and damping fluctuations. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical method to analyze a two-hinged beam with elliptical arched bottom subjected to two concentrated loads. The two-hinged beam is a statically indeterminate structure to the first degree. Therefore, it is not possible to calculate the reactions and internal forces in the ordinary method by using equilibrium equations alone. Towards this end, the strain energy stored in the Hinged-hinged beam during deformation is given, considering the change of the cross-section along the length of the beam. The Gaussian Quadrature method was used to perform numerical integration to obtain the Horizontal Thrust for non-prismatic members. Also, a comparison was made between the proposed method and the experimental results that are shown by some authors. The comparison shows rather good agreement between the theoretical and experimental ultimate loads of the beams with an elliptical-arched bottom. The difference ratio of the ultimate load between theoretical data and experimental data was recorded from (1.13-1.29). [ABSTRACT FROM AUTHOR]

The nonlinear dynamic analysis has been carried out to investigate the dynamic behavior of a perfectly balanced horizontal rotor (HR)-tilting pad journal bearing (TPJB) system and perfectly balanced vertical rotor (VR)-tilting pad journal bearing (TPJB) system by computing frequency response of both the systems. To do so, governing differential equations (GDEs) of motion for HR-TPJB system and VR-TPJB system has been derived and they were solved by finite element method (FEM). The GDE of motion of both systems have been combined to form a unit set. This unit set represents the HR/VR-TPJB system. Implementation of computational numerical integration technique has been employed to solve equations of motion of both the systems which has been solved using the MATLAB® ODE-15s solver. Indigenous MATLAB® program has been created to compute the above-mentioned frequency response of the system efficiently. Time-Amplitude Response and Frequency-Amplitude Response with Phase at both the TPJB's and rigid disc locations have been computed by Fast Fourier Transform (FFT). The dynamic behavior of the perfectly balanced HR-TPJB and VR-TPJB systems have been analyzed for different rotor speeds. The results and discussions on the nonlinear dynamic behavior of perfectly balanced HR-TPJB and VR-TPJB systems operating at low and high rotor speed have been explained which indicates HR-disc is more unstable than HR-journal inside identical 4-pad TPJBs at low rotational speed (1500 rpm). The frequency response of both HR-TPJB system and VR-TPJB system at low speed (1500 rpm) shows that peak amplitude appeared much before in VR than HR, which indicates even in low rotational speed, VR-TPJB system is more unstable than HR-TPJB system. Results demonstrated that the balanced VR operated at high speed (6000 rpm) is more prone to instabilities than its horizontal counterpart (HR-TPJB system) at the same speed (6000 rpm). [ABSTRACT FROM AUTHOR]

In this study the nonlinear vibrations of an electromagnetic actuated cantilever are explored. The nonlinear differential equation is solved by means of the Optimal Homotopy Asymptotic Method (OHAM). Comparisons between results obtained using our procedure and those of numerical integration show the effectiveness and reliability of our approach. [ABSTRACT FROM AUTHOR]

The last decades have been showing an explosive development in optimization techniques and implementation of interdisciplinary optimizations in aircraft design within various systems engineering and concurrent engineering analyses. The quality of the optimization calculations depends on availability of large amounts of data describing the modeled processes; hence obtaining fast solutions of dynamic models continues to be of significant interest. Many purely numerical integration methods have been proposed during the last decades and some matured and grown into new practical algorithms; however, limits exists that cannot be exceeded by numerical simulations alone, hence the interest in the (semi)analytical solutions have been re-growing as well. The current paper addresses the ordinary differential equations that governs the longitudinal maneuvers of airplanes and includes both purely numerical integrations and approximate analytical solutions. The analytical solutions are based on linearized equations, some of which are provided by small perturbation lgorithms.. [ABSTRACT FROM AUTHOR]

This article presents the non-linear control approach using the high-order numerical integration method based on the Taylor series. The selected example (the magnetic levitation system) is analyzed and controlled using a non-linear controller. The results are compared with the state-of-the-art solvers in MATLAB. [ABSTRACT FROM AUTHOR]

We consider initial value problems for ε2φ″ + a(x) φ = 0 in the highly oscillatory regime, i.e., with a(x) > 0 and 0 < ε ≪ 1. We discuss their efficient numerical integration on coarse grids, but still yielding accurate solutions. The O(h2) one-step method from [2] is based on an analytic WKB-preprocessing of the equation. Here we extend this method to O(h3) accuracy. [ABSTRACT FROM AUTHOR]

This paper studies the problem of construction of the optimal quadrature formula for numerical calculation of Fourier integrals. Applying the discrete analogue of the differential operator d 4 d x 4 − 2 d 2 d x 2 + 1 and using its properties we obtain the optimal quadrature formula wich is exact for hyperbolic functions sinh(x) and cosh(x), we get explicit expressions for the coefficients of the optimal quadrature formula. The obtained optimal quadrature formulas can be used in problems where Fourier transformations are used. [ABSTRACT FROM AUTHOR]

This paper describes in detail the method and algorithm for calculating the numerical integration of non-stationary two-dimensional systems of Navier-Stokes equations for a compressible gas using high-order implicit (explicit) difference schemes, i.e., the Beam-Warming difference scheme. A number of mathematical transformations, such as non-dimensionalization of coordinates and physical parameters, transforming the shape of the channel into a square one, as well as thickening the integration steps with large gradients of unknowns, which make it possible to bring problems to a model one for solving similar problems. In addition to the study, as convergence in the number of calculated points, the dependence of the number of iterations on the Courant number and comparison of the results obtained by different proposed models for calculating the effective viscosity, as well as a number of numerical studies as co-occurrence, temperature inhomogeneities, non-design, the ratio of the sizes of the inlet slots of cocurrent flows and the length of the channel to the height of the main flow and the degree of expansion of the channel to the process of mixing and distribution of flows in the channel. It was revealed at what ratios of the initial parameters of the cocurrent flows and the linear dimensions of the channel a recirculation zone is formed. For a channel of constant cross section at large ratios of velocities (72, 46) and temperature (2, 33), as well as small ratios of the channel length to the height of the inlet slot of the main flow (5, 31), even at the same jet pressures in the initial section, the recirculation zone occupies more than 55% of the input section, and the length along the longitudinal coordinate reaches 20 cm. [ABSTRACT FROM AUTHOR]

Vibrational nonequilibrium of diatomic molecules resulting in non-Boltzmann distributions is a phenomenon commonly encountered in rapid hypersonic nozzle expansions. The usual assumption of different vibrational temperatures for different species cannot simulate such nonequilibrium behaviour. State-to-state models governed by a master equation describe the evolution of population number for all vibrational levels. These equations possess singularly perturbed characteristics and stable numerical integration must account for this stiffness. Linearly implicit, or Rosenbrock–Wanner (ROW), integration methods are inherently more stable than explicit methods and less computationally complex than implicit ones of equivalent order. One historical limitation of ROW methods is the requirement that the exact Jacobian of the evolution rate vector must be computed to achieve classical order of convergence. This may be analytically intractable for large systems. Automatic Differentiation (AD) provides a solution by algorithmically determining the exact derivatives, to working precision, based upon implementations of the rate vector. State-to-state simulations of carbon monoxide vibrational kinetics under the influence of sudden a reduction in transitional/rotational temperature using linearly implicit time integration with AD is presented. Computational performance of the ROW method is compared to second-order backward-difference integration. [ABSTRACT FROM AUTHOR]

The sensitivity of expected annual damage, EAD, is analytically analysed by applying a log-linear relation between return periods and corresponding damages. It is found that the smallest return period for damage should be estimated as precisely as possible, that the percentage uncertainty in the damage estimate is transformed into the same percentage uncertainty in the EAD estimate, and that it is possible to extrapolate beyond the largest return period with corresponding damage assessment. The precision of the estimate of EAD is investigated in detail in the case of only few available data, and it is found that two different methods for numerical integration may result in strongly diverging results. By applying a piecewise log-linear damage function, it is shown that the log-linear model provides a trustworthy estimate of EAD, also in the case of few available data. Finally, the modifications needed in the special case of threshold exceedance data instead of annual maxima data are presented. [ABSTRACT FROM AUTHOR]

The primary purpose of this study is to develop a rule for determining the values of double integrals, its integrals with continuous integrands but have singularity at partial derivatives, numerically using the Trapezoidal rule, you are not at the end of the integration region. with the two dimensions x and y. and the derive the correction error terms and we used Romberg acceleration [3], [9] to enhance the outcomes when the number of sub-intervals, the sub-intervals in the direction of dimension y are equal to sub-intervals in the direction of dimension x. We'll refer to this method as RTT, and we can rely on it because it produced high precision results in terms of analytical integration values and small sub-intervals. [ABSTRACT FROM AUTHOR]

For a number of years, numerical integration of the aircraft's equation of motion seemed very well established. Virtually no new studies have been dedicated to this topic, while a significant amount of efforts have been dedicated to improving optimization algorithms, and to implementing optimization algorithms in various design and analysis procedures. However, the quality of the results in many optimization procedures depends upon the availability of high amounts numerical data which is often obtained from numerical simulations, hence availability of faster integration algorithms became once again of interest. The current paper discusses a method of utilizing a short arcs analytical solution of airplane's longitudinal channel equations to accelerate the numerical integration. [ABSTRACT FROM AUTHOR]

The paper deals with the use of high-order numerical integration method in the area of system control. The selected nonlinear technical problem – pendulum is analysed and the control system using the high-order numerical integration method based on the Taylor series is implemented and compared with the state-of-the-art numerical integration methods implemented in MATLAB software. [ABSTRACT FROM AUTHOR]

This talk considers the numerical treatment of the differential equation that describes the motion of electric particles in a strong magnetic field. A standard integrator is the Boris algorithm which, for small stepsizes, can be analysed by classical techniques. For a strong magnetic field the solution is highly oscillatory and the numerical integration is more challenging. New modifications of the Boris algorithm are discussed, and their accuracy and long-time behaviour are studied with means of modulated Fourier expansions. Emphasis is put on the situation where the stepsize is proportional to (or larger than) the wavelength of the oscillations. [ABSTRACT FROM AUTHOR]

We present some results on the numerical preservation of invariant laws characterizing the underlying dynamics of stochastic problems, described by Itô stochastic differential equations. Our approach follows the spirit of the so-called stochastic geometric numerical integration. We first address the nonlinear stability properties of stochastic theta-methods with respect to mean-square dissipative nonlinear test problems, generating a mean-square contractive behaviour. The pursued aim is that of making the same property visible also along the numerical discretization via stochastic θ -methods: this issue is translated into sharp stepsize restrictions depending on some parameters of the problem. We next consider nonlinear damped stochastic oscillators. In particular, we are interested in accurately maintaining the stationary densities of the position and the velocity of a particle driven by a nonlinear deterministic forcing term and an additive noise as stochastic forcing term. The provided analysis relies on a linearization of the nonlinear problem, whose effectiveness is proved theoretically and numerically confirmed. [ABSTRACT FROM AUTHOR]

In this article, attention is paid to the mathematical modeling of the ball lightning temperature field. The relevance of the work is due to the fact that the phenomenon itself is common, but in itself has not been sufficiently studied. Various models are used to describe its properties. In the article, ball lightning is considered as a plasma ball. The main purpose of the work is mathematical modeling of the lightning temperature field taking into account radiation heat transfer. Modeling of the thermal process is based on numerical integration of the heat equation. Also, based on the obtained result, an analysis of the behavior of the temperature field was carried out. [ABSTRACT FROM AUTHOR]

Significant advances in modeling and simulations for microwave reflectometry have been conducted in recent years. An example is the integration of improved numerical descriptions of magneto-hydrodynamics (MHD) instabilities, obtained from MHD codes, together with 2D full-wave codes to implement synthetic reflectometry diagnostics in realistic conditions. In particular, the nonlinear MHD code JOREK has been used previously together with the 2D full-wave code REFMUL, to assess the response of conventional O-mode reflectometry along a Type-I edge localized mode (ELM) crash. In this work, a similar framework and synthetic diagnostic set-up are considered but with an extended MHD simulation where a Type-I ELM cycle comprised of several ELM crashes is studied. This includes the self-consistent MHD evolution along inter-ELM periods, which was absent in the previous study. The reflectometer response at the mid-plane of the low magnetic field side is used to provide information about the behavior of density fluctuations along the full ELM cycle. The inter-ELM periods display density fluctuations in agreement with the ELM triggering mechanisms manifesting as reflectometry signatures which are identified with ELM precursors. The precursor signatures are observed a few milliseconds before a transition from linear to non-linear reflectometry regimes occurs, associated with the explosive onset of the ELM. [ABSTRACT FROM AUTHOR]

The paper explores numerically the nonlinear dynamic response of simply supported axially travelling beam The governing equation of motion is nondimensionalized and then truncated into a set of gyroscopically coupled nonlinear ordinary differential equations via Galerkin approach. Numerical computation is performed via 4th order Runge-kutta numerical integration method to examine the effect of non-dimensional velocity on dynamic response of axially travelling beam through time trace, phase plane and frequency spectra. The numerical simulations indicate that the system exhibits both periodic and quasiperiodic oscillations [ABSTRACT FROM AUTHOR]

To analyse the Potassium (K+) ion concentration and channel effects in ventricular Electrocardiogram (ECG) generation for normal and arrhythmic conditions using the euler integration method. In this research human ventricular cells are taken based on the model of the human endocardial and epicardial cells by the Ten Tusscher, Nobel and Panflov (TNP model). Model is modified and interpredicted based on the experimental data of Han, describing the properties of K+ concentrations and channel dynamics in the ventricular ECG generation. Euler integration numerical method is used to analyse the TNP model for different channel and ion concentration failure conditions in the same group of 100 samples. Results: The normal intracellular K+concentration (K+) value is 138.3mM which having Action Potential (AP) mean value in the range of -70mV to 38mV, but for different abnormal such as (25%= 172.5mM, 50%=207mM, 100%=276.6mM) having AP of mean values like (25%=-19mv to 35mv, 50%= -18mv to 37mv, 100%=-16mv to 37.5mv). Similarly, its K+ membrane current mean values like K+ transient outward current (Ito), K+ inward current (IK1), K+ rapid current (Ikr) and K+ slow current (Iks) is having variations with respect to normal K+ membrane current. Out of all membrane currents Iks is having more effects in mean membrane current with respect to membrane currents (-0.149pA to -0.19pA with -0.04 to 0.05pA). Conclusion: This type of K+ membrane currents variations lead to delayed afterdepolarization (DAD) and in turns produce deep long ST segment waves, more deep negative T waves and absence of T waves in ventricular ECG. [ABSTRACT FROM AUTHOR]

Most of the works in the literature agree to attribute the generation of wheel/rail squeal noise in curves to the important lateral slip imposed in the curve and the resulting instabilities. In models, the occurrence of the phenomenon is thus generally studied through a stability analysis based on the linearization of the contact forces. Despite its undeniable interest, the stability analysis does not allow the prediction of the amplitudes of the nonlinear self-sustained vibrations resulting from the instabilities. These nonlinear vibrations are most often calculated using a numerical integration of the dynamic equations of the system in the time domain. Some authors have proposed simplified methods allowing a direct calculation of stationary regimes, but limited to a reduced modal description of the system dynamics. In this presentation, an original method is proposed to determine approximate limit cycles from the wheel/rail contact mobilities expressed in the frequency domain. The contact condensation allows to be both more general and more functional to describe the dynamics of structures, in particular the one of the rail. Assuming a mono-harmonic vibratory cycle, the corresponding amplitude is determined from a power balance and the squeal level at the considered pulsation is obtained from analytical radiation factors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce modified rule for numerical integration of data points. This method depending on geometric mean calculations of used points in our interval. For testing the accuracy of our method. Many comparisons are calculated. The results of this method give high accuracy. [ABSTRACT FROM AUTHOR]

In this article the authors consider the motion patterns of how a material particle is moved with a spiral surface in a random direction when the spiral rotates. To obtain the equation of motion, all forces are considered, including the inertia forces applied to the particle on the helical line of the spiral, axis has been considered, which characterizes the geometric characteristics of the helix, a cylindrical casing and particle size in the spiral and helical device. To obtain data on the nature of particle motion, numerical integration of the obtained equations for spiral devices with various parameters was performed. [ABSTRACT FROM AUTHOR]

In this article, attention was paid to the mathematical modeling of the plasma temperature field under boundary conditions of the third kind. The simulation of the thermal process is based on the numerical integration of the thermal conductivity equation. This takes into account the change in the thermal conductivity of the plasma and convective heat transfer. Based on the obtained result, the behavior of the temperature field is analyzed. [ABSTRACT FROM AUTHOR]

In this paper a RKN method of sixth algebraic order is constructed, based to the nullification of the phase-lag, amplification error and to their derivatives. [ABSTRACT FROM AUTHOR]

A vocal fold model is analytically investigated with the help of an analytical technique, namely the Optimal Homotopy Asymptotic Method (OHAM). An explicit and very accurate analytical solution is obtained and the accuracy of the results is proved for a set of physical parameters by means of comparisons with numerical integration results. The proposed approach may be easily extended to deeper investigations of vocal fold models. [ABSTRACT FROM AUTHOR]

Numerical integration of the aircraft's equation of motion has become routine for many decades, the basics are covered in virtually any undergraduate program and, for a while, no further studies seemed to be needed in this topic. On the other hand, many researchers dedicated their efforts to improving optimization algorithms, and nowadays, many modern design procedures include optimization algorithms, however, many of this optimization procedure require analyzing large amounts of data, much of which is provided by numerical simulations of the aircraft's behavior. Consequently, obtaining faster integration algorithms became once again of interest. The current paper discusses a method of utilizing an analytical solution of the small perturbation linearized equations to accelerate the numerical integration of airplane's longitudinal equations of motion. [ABSTRACT FROM AUTHOR]

The paper describes the high order numerical integration method based on the Taylor series. The positive properties of the method are demonstrated on the control system of the DC motor. The numerical solution of the system is performed using the state-of-the-art numerical solvers in MATLAB and the high order method. The results are compared and analyzed. [ABSTRACT FROM AUTHOR]

The numerical solution of ordinary differential equations having oscillating solution may require very small stepsizes when the frequency of oscillation increases. In order to develop efficient and accurate numerical methods, it is convenient to use adapted numerical integration based on the exploiting a-priori known information about the behavior of the solution. We present a class of exponentially fitted peer methods, show the derivation of order conditions and compare them with classical peer methods. [ABSTRACT FROM AUTHOR]

At the initial stage of the creation of new types of launch vehicles, the so-called design ballistic calculations are carried out. The main purpose of these calculations - is to make the choice of optimal combinations of the main design parameters. Currently, the relevance of the project ballistics tasks has grown significantly in the connection with the research of the new generation of launch vehicles, which are related to both the problems of deep space exploration and the creation of low-orbit satellite constellations of small spacecraft. In the process of the design methods developing, models of motion should not be inferior to the uncertainties of the source data. So, the algorithms of these methods should reflect the correlation of design parameters with the flight characteristics of the launch vehicle. Above principles were put as the basis of the proposed correlations linking the values of the trajectory variables at the end of the launching phase of the first stages of launch vehicles with the main design parameters. The calculated dependences are based on the results of the analysis of a large number of trajectories, which are corresponding to variations of different studied factors. The calculations were carried out by the method of numerical integration of differential equations of motion in a wide range of variation of the source data. The analysis done gave us the possibility to identify some general patterns of controlled motion of a material point and to obtain the structure of calculation formulas in an analytical form. [ABSTRACT FROM AUTHOR]

Sensitivity studies are nowadays applied to some of the most complicated mathematical models from various intensively developing areas of application. Such a sophisticated model in the area of air pollution modeling is the Danish Eulerian Model, a powerful large scale air pollution model with a long development history. Over the years it was used successfully in different long-term environmental studies for the European region. In this talk we discuss some performance-critical achievements in the parallel optimization and a systematic approach for sensitivity analysis of the latest version of the Danish Eulerian Model, UNI-DEM. A comprehensive experimental study of Monte Carlo algorithms based on Latin Hypercube Sampling and Adaptive approach for multidimensional numerical integration has been done. The algorithms have been successfully applied to compute global Sobol sensitivity measures, corresponding to the influence of several input parameters on the concentrations of some of the air pollutants of highest importance. The numerical tests show that the Monte Carlo algorithms under consideration are efficient for the multidimensional integrals in this study. [ABSTRACT FROM AUTHOR]

This paper presents a study of the evolution the study of the product of two normally distributed variables. From first approaches in the middle of the 20th Century until the most recent ones from this decade. Nowadays, existence of an unique formula for the product was not proved. Partial results using different approaches: Bessel Functions, Numerical Integration, Pearson Type Function, … [ABSTRACT FROM AUTHOR]

In this paper, it is presented the dependence of calculation and speed of calculation when increasing integration points in the finite element of the enrichment type, which is used in the eXtended Finite Element Method (XFEM). The Legendre polynomial was used to increase the number of integration points and the Gauss quadrature was used for integration. A simple 3D model consisting of hexahedron was created for testing. [ABSTRACT FROM AUTHOR]

The ITER Radial Neutron Camera (RNC) is a diagnostic system designed as a multichannel detection system to measure the uncollided neutron flux from the plasma, generated in the tokamak vacuum vessel, providing information on neutron emissivity profile. The RNC consists of array of cylindrical collimators located in two diagnostic structures: the ex-port system and the in-port system. The in-port system, contains the diamond detectors which need a temperature protection. Feasibility study of the efficiency of the cooling system for the In-port Detector Modules of the RNC during baking process was the main goal of thermo-hydraulic numerical modeling. The paper presents the concept of the cooling system layout and the original way of integration of numerical thermo-hydraulic analyses of the in-port detector cassette. Due to the large extent of the detector cassette it is impossible to include all relevant thermal and hydraulic effects in one global model with sufficient level of details. Thus the modelling strategy is based on the concept of three stage modelling from details to global model. The presented paper includes results of numerical calculations made with ANSYS Fluent software in order to provide the final answer, including calculation of heat loads in the detector cassette from adjacent walls during baking and normal operation conditions. [ABSTRACT FROM AUTHOR]

In this paper, a new mesh generation technique is used to evaluate the surface integral problem over polygonal domain, applying Gauss Legendre quadrature rule for every four noded quadrilateral elements and extract Gaussian points and weights, the proposed method gives more accurate results compare to existing one. [ABSTRACT FROM AUTHOR]

In the present study, we report the kinetic analysis of the polyindole modified metal (Au) as a glucose sensor utilizing Surface Plasmon Resonance (SPR) technique. Polyindole (PIn) was deposited by spin coating to modify the surface of the gold disc. Sensor surface was prepared by immobilizing glucose oxidase (GOD) on the polyindole modified gold disc. Different concentrations of glucose were taken to analyze the sensor response. A change in refractive index of the film was observed due to the chemical reactions of glucose with glucose oxidase. The response of the sensor is fast and highly sensitive to low concentrations of glucose and the sensitivity increases in the range of 0.1-0.5 µM.The sensogram of glucose sensor on Polyindole active surface was analyzed using kinetic evaluation software for three different concentration of glucose 0.1μM, 0.25μM, and 0.5μM. Association phase analysis was done on analysis wizard using both integration and numerical integration rate method and it was done for monophasic and biphasic system of interaction for all the three concentration of glucose. The kinetic evaluation is done invariably using monophasic model, which involves 1:1 interaction. In the present study, the biphasic model of interaction, which involves a non-linear fitting, is giving a better analysis. This change can be attributed to the binding sites with different affinities. [ABSTRACT FROM AUTHOR]

This paper considers two procedures to estimate the fuzzy reliability for Lomax distribution. The first procedure depends on fuzzy reliability definition that uses the composite trapezoidal rule in order to find the numerical integration and the second is Bayesian procedure which includes different cases depends on sample data and hyper-parameters of prior gamma distribution with symmetric and asymmetric loss functions. [ABSTRACT FROM AUTHOR]

In this study the application of the sinc-Galerkin method to an approximate solution of integrodifferantial problem were discussed. Applying this method the integrodifferential equation is reduced to a system of algebraic equations without any numerical integration. Numerical example is provided to illustrate the accuracy and efficiency of the method. [ABSTRACT FROM AUTHOR]

A numerical solution of the Fredholm integral equations can be obtained by many methods. Most of them lead to a solution of a system of linear equations with fully populated matrices. In the case of collocation or product integration methods, each element of the matrix is an integral, which needs to be calculated. It causes high computing time in multidimensional problems. Computing time can be reduced by the Nyström method. It is based on substitution of the integral by a numerical integration rule. It has the advantage that only diagonal elements of the matrix are integrals. When the kernel function is singular, a singularity subtraction is needed. However it can not be used for every kernel function and every integration rule. The main point of this paper is the convergence conditions of the Nyström method as applied to a special multidimensional integral equation. The paper includes an illustrative example. [ABSTRACT FROM AUTHOR]

In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We focus on methods of the special case that use only one f evaluation. We construct two methods of sixth and one method of seventh order with four and five stages and minimum phase-lag and amplification error. [ABSTRACT FROM AUTHOR]

Analytical solutions to integrals are far more useful than numeric, however, the former is not available in many cases. We evaluate integrals indicated in the title numerically that are necessary in some approaches in quantum chemistry. In the title, where R stands for nucleus-electron and r for electron-electron distances, the n, m= 0 case is trivial, the (n, m)= (1,0) or (0,1) cases are well known, a fundamental milestone in the integration and widely used in computational quantum chemistry, as well as analytical integration is possible if Gaussian functions are used. For the rest of the cases the analytical solutions are restricted, but worked out for some, e.g. for n, m= 0,1,2 with Gaussians. In this work we generalize the Becke- Lebedev-Voronoi 3 dimensions numerical integration scheme (commonly used in density functional theory) to 6 and 9 dimensions via Descartes product to evaluate integrals indicated in the title, and test it. This numerical recipe (up to Gaussian integrands with seed exp(-|r1|²), as well as positive and negative real n and m values) is useful for manipulation with higher moments of inter-electronic distances, for example, in correlation calculations; more, our numerical scheme works for Slaterian type functions with seed exp(-|r1|) as well. [ABSTRACT FROM AUTHOR]

Development of new time integration schemes for problems of structural dynamics reflects the progress both in the numerical mathematics and in the information technology. Some results from the last several years bring the new insights into such schemes and the convergence of related algorithms. This paper pays attention namely to the unified approach to the promising composite schemes, containing various numerical integration and differentiation procedures. [ABSTRACT FROM AUTHOR]

The problem of structure-foundation interaction involves solving system of PDEs with pressure only contact condition. In the past, many numerical methods were used to solve this problem including the combination of finite element method with meshless convolution of fundamental solution, which is discussed in this paper. A practical application of this approach is presented with focus on efficient algorithm for solving the convolution integral. [ABSTRACT FROM AUTHOR]

The multi-measures model applied to cosmology has been recently shown to reproduce qualitatively the expected stages of the Universe evolution, along with some unexpected features. In this article, we continue its exploration with a detailed study of the effective potential of the model. An analysis of the limits of applicability of the effective potential show that during most of the Universe evolution, the effective potential is a very good approximation of the actual potential term. There is, however, a deviation between the two occurring in the earliest moments of the evolution, which has an important role on the behavior of the inflaton scalar field. In the studied cases, during this initial time, the inflaton is increasing in absolute value, which seems consistent with “climbing up” the effective potential. To investigate this behavior, we use numerical integration to find the numerical potential and we show that during the early stage of the evolution, the shape of the numerical potential is very different from that of the effective one and instead of a left plateau followed by steep slope, one observes only a slope with additional local maximum and minimum. This result demonstrates that for complicated equations of motion of the inflaton, one should not rely only on the notion of kinetic and effective potential terms to describe the problem as they may not be accurate in the entire numerical domain. [ABSTRACT FROM AUTHOR]

Many differential equations of Dynamics (i.e. Celestial Mechanics, Molecular Dynamics, and so on) one can reduce to polynomial form, i.e. to system of differential equations with polynomial (in unknowns) right-hand sides. It implies that at every step of numerical integration of these equations, one needs to evaluate many different multivariate monomials for many values of variables, and that is why minimizing the evaluation cost of a system of monomials in the right-hand sides is an important problem. In Alesova, Babadzanjanz, et al., “Schemes of Fast Evaluation of Multivariate Monomials for Speeding up Numerical Integration of Equations in Dynamics” (AIP, volume 1978, issue 1, 2018) we considered a scheme of successive multiplications minimizing the total cost of evaluation of multivariate monomials of a system of monomials and the algorithm, which for a given system of third order monomials reduces the original problem to the linear programming problem, and computes such a scheme. Then we proposed the algorithm and the corresponding Mathematica program that, given an arbitrary system of multivariate cubic monomials constructs the linear programming problem mentioned. We have also presented the results of corresponding numerical experiments and have shown that the total evaluation cost of systems of monomials has reduced substantially. An important requirement for the process of solving differential equations in Dynamics is high accuracy at large time intervals. One of effective tools for obtaining such solutions is the Taylor series method. In Alesova, Babadzanjanz, et al., “High-Precision Numerical Integration of Equations in Dynamics” (AIP, volume 1959, issue 1, 2018) we considered the equations of the N-body problem in various polynomial forms (with and without additional third order polynomial perturbations). This allowed us to obtain effective algorithms for finding the Taylor coefficients, a priori error estimates at each step of integration, and an optimal choice of the order of the approximation used. Moreover, we considered a number of corresponding numerical experiments, which showed the effectiveness of the Taylor series method implementation presented. In present work, we generalize the results mentioned above on the case of systems of multivariate fifth order monomials (using in corresponding numerical experiments differential equations of the N-body problem with additional fifth order polynomial perturbations). [ABSTRACT FROM AUTHOR]

The aim of this article is the studying of the "predator-prey" populations controlled interaction. The well-known Lotka-Volterra system ([1], [3], [5-15]) with control is used as a mathematical model. A complete research of this model is done: from its parameters identification to the choice of optimal control. The identification numerical algorithms are based on the Taylor series method. This method application is reasonable in this case, because right sides of the considered ODEs system can be presented in polynomial form. To select the best control, a number of algorithms based on the direct search are proposed. They allow to find the optimal ratio between the time, cost and accuracy of the perturbed system's returning to the equilibrium point. These algorithms are: the control's work areas constructing algorithm; the algorithm for the constructing a dependence the control’s cost of the distance to the target point; the algorithm for the constructing a dependence the distance of the control’s cost. The algorithms are implemented in the Matlab package and are tested on model examples. Analysis of the test results allows us to see changes in the system dynamics because of control, to compare control influences and choose from them the optimal one for the "quality – cost" balance. [ABSTRACT FROM AUTHOR]

The present project deals with a method of designing a photovoltaic solar pumping system. The aim of this design is to make an optimal choice of the various industrial equipment of this system ensuring optimization, regulation and safety. This sizing method is based on the mathematical equations that govern the system as well as the charts of electrical and mechanical quantities. The system in question is composed of three equipments: The Photovoltaic generator, the solar inverter drive and the motor pump group. This design not only makes it possible to design the pumping system to meet the desired technical specifications, but also to ensure compatibility to ensure proper operation and reliability. It is based essentially on the assessment of the water requirements, the calculation of the necessary hydraulic energy, the calculation of the necessary electrical power, that provided by the PV generator and the optimization of the constituents of the pumping system. The design and choice of elements are made on a real installation to meet the water needs of the gardens of the Faculty of Science and Techniques of Beni-Mellal. Thus, the estimated flow rate is 3.5 m³ / h for a total dynamic head of 65 m. [ABSTRACT FROM AUTHOR]

In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We construct methods with variable coefficients that depend on the frequency of the specific problem. [ABSTRACT FROM AUTHOR]

In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We compare numerical methods with constant and variable coefficients. [ABSTRACT FROM AUTHOR]

In this work we consider Two Derivative Runge-Kutta methods for the numerical integration of oscillatory problems. We construct methods with variable coefficients that depend on the frequency of the specific problem. [ABSTRACT FROM AUTHOR]