Numerical solutions of integral equations for electromagnetics

2020 ◽  
pp. 359-380
Author(s):  
Roberto D. Graglia ◽  
Andrew F. Peterson
Keyword(s):  
Integral Equations ◽  
Numerical Solutions

A stochastic operational matrix method for numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations

2020 ◽  
Vol 28 (3) ◽  
pp. 209-216
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Volterra Integral Equations ◽  
Numerical Examples ◽  
Operational Matrix Method ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix ◽  
Block Pulse Function

AbstractIn this article, hybrid Legendre block-pulse functions are implemented in determining the approximate solutions for multi-dimensional stochastic Itô–Volterra integral equations. The block-pulse function and the proposed scheme are used for deriving a methodology to obtain the stochastic operational matrix. Error and convergence analysis of the scheme is discussed. A brief discussion including numerical examples has been provided to justify the efficiency of the mentioned method.

scholarly journals Numerical Solutions of Fredholm Integral Equations Using Bernstein Polynomials

2010 ◽  
Vol 2 (2) ◽  
pp. 264-272 ◽  
Author(s):  
A. Shirin ◽  
M. S. Islam
Keyword(s):  
Integral Equation ◽  
Galerkin Method ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Numerical Solutions ◽  
Bernstein Polynomials ◽  
Fredholm Integral Equations ◽  
Matrix Formulation ◽  
Piecewise Polynomials ◽  
The Galerkin Method

In this paper, Bernstein piecewise polynomials are used to solve the integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are used as the approximation of basis functions. Examples are considered to verify the effectiveness of the proposed derivations, and the numerical solutions guarantee the desired accuracy.  Keywords: Fredholm integral equation; Galerkin method; Bernstein polynomials. © 2010 JSR Publications. ISSN: 2070-0237 (Print); 2070-0245 (Online). All rights reserved. DOI: 10.3329/jsr.v2i2.4483               J. Sci. Res. 2 (2), 264-272 (2010) 

scholarly journals On the numerical solutions for nonlinear Volterra-Fredholm integral equations

2022 ◽  
Vol 40 ◽  
pp. 1-11
Author(s):  
Parviz Darania ◽  
Saeed Pishbin
Keyword(s):  
Nonlinear System ◽  
Integral Equations ◽  
Numerical Experiments ◽  
Numerical Solutions ◽  
Coefficient Matrix ◽  
Collocation Methods ◽  
Fredholm Integral Equations ◽  
Stability Estimates ◽  
Lower Triangular ◽  
Theoretical Results

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

AN EFFICIENT NUMERICAL APPROACH FOR SOLVING ABEL’S INTEGRAL EQUATIONS BY USING MODIFIED TAYLOR WAVELETS

2021 ◽  
Vol 10 (5) ◽  
pp. 2285-2294
Author(s):  
A. Kumar ◽  
S. R. Verma
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
Numerical Approach ◽  
Algebraic Equations ◽  
Wavelet Method

In this paper, a modified Taylor wavelet method (MTWM) is developed for numerical solutions of various types of Abel's integral equations. This method is based on the modified Taylor wavelet (MTW) approximation. The purpose behind using the MTW approximation is to transform the introduction problems into an equivalent set of algebraic equations. To check the accuracy and applicability of the proposed method, some examples have been solved and compared with other existing methods.

Stochastic operational matrix of Chebyshev wavelets for solving multi-dimensional stochastic Itô–Volterra integral equations

2019 ◽  
Vol 17 (03) ◽  
pp. 1950007 ◽  
Author(s):  
S. Singh ◽  
S. Saha Ray
Keyword(s):  
Integral Equations ◽  
Numerical Solutions ◽  
General Procedure ◽  
Operational Matrix ◽  
Volterra Integral Equations ◽  
Algebraic Equations ◽  
Chebyshev Wavelets ◽  
System Of Integral Equations ◽  
Block Pulse Functions ◽  
Stochastic Operational Matrix

In this paper, the numerical solutions of multi-dimensional stochastic Itô–Volterra integral equations have been obtained by second kind Chebyshev wavelets. The second kind Chebyshev wavelets are orthonormal and have compact support on [Formula: see text]. The block pulse functions and their relations to second kind Chebyshev wavelets are employed to derive a general procedure for forming stochastic operational matrix of second kind Chebyshev wavelets. The system of integral equations has been reduced to a system of nonlinear algebraic equations and solved for obtaining the numerical solutions. Convergence and error analysis of the proposed method are also discussed. Furthermore, some examples have been discussed to establish the accuracy and efficiency of the proposed scheme.

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