Methods and effective algorithms for solving multidimensional integral equations
Российский технологический журнал, 2022 Objectives. Integral equations have long been used in mathematical physics to demonstrate existence and uniqueness theorems for solving boundary value problems for differential equations. However, despite integral equations have a number of advantages in
A. B. Samokhin
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Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula [PDF]
Applied Optics, 2006 The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical
Shen, F. B., Wang, Anbo
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High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: $\mathcal{O}(1)$ Sampling Cost via Incident-Field Windowing and Recentering [PDF]
, 2020 This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains.
Anderson, Thomas G. +2 more
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Friction Reduction Due to Heating in the Sliding Contact of Smart Coating: Modeling of Mutual Effect
Lubricants, 2022 In smart coatings designed for friction units operating in wide temperature ranges, the material reacts to heating by changing its frictional properties. Appropriate experimental studies are available.
Elena Torskaya, Fedor Stepanov
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New operational relations for mathematical models of local nonequilibrium heat transfer
Российский технологический журнал, 2022 Objectives. Recently, interest in studying local nonequilibrium processes has increased in the context of the development of laser technologies, the possibility of reaching ultrahigh temperatures and pressures, and the need for a mathematical description
E. M. Kartashov
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Numerical Integral Transform Methods for Random Hyperbolic Models with a Finite Degree of Randomness [PDF]
Mathematics, 2019 This paper deals with the construction of numerical solutions of random hyperbolic models with a finite degree of randomness that make manageable the computation of its expectation and variance. The approach is based on the combination of the random Fourier transforms, the random Gaussian quadratures and the Monte Carlo method.
M. Consuelo Casabán +2 more
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Comparison between variational iteration method and Gegenbauer–Galerkin method for solving two dimensional nonlinear Volterra integral equations of the second kind [PDF]
AIP AdvancesThis paper intends to introduce two numerical techniques—the variational iteration method and the Gegenbauer–Galerkin method—for obtaining solutions to two dimensional nonlinear Volterra integral equations of the second kind.
M. H. Ahmed
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A bi‐cubic transformation for the numerical evaluation of the Cauchy principal value integrals in boundary methods [PDF]
International Journal for Numerical Methods in Engineering, 1989 AbstractThe numerical strategies employed in the evaluation of singular integrals existing in the Cauchy principal value (CPV) sense are, undoubtedly, one of the key aspects which remarkably affect the performance and accuracy of the boundary element method (BEM).Thus, a new procedure, based upon a bi‐cubic co‐ordinate transformation and oriented ...
Cerrolaza Rivas, Miguel +1 more
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Frontiers in Physics, 2018 In this paper, the operators of fractional integration introduced by Marichev-Saigo-Maeda involving Appell's function F3(·) are applied, and several new image formulas of generalized Lommel–Wright function are established.
Ritu Agarwal +4 more
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Use of the repeated integral transformation method to describe the transport of solute in soil
Heliyon, 2023 Predicting the fate and transport of contaminants in soil or groundwater systems using analytical or numerical models is crucial for environmental researchers.
Elias Mwakilama +2 more
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