scholarly journals Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

2019 ◽  
Vol 9 (2) ◽  
pp. 471-480 ◽  
Author(s):  
Y. H. Youssri ◽  
R. M. Hafez
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Chebyshev Polynomials ◽  
Matrix Equation ◽  
Chebyshev Collocation ◽  
Chebyshev Nodes ◽  
Potential Applicability ◽  
The Given

Abstract This work reports a collocation algorithm for the numerical solution of a Volterra–Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss–Chebyshev nodes were then used to reduce the Volterra–Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

scholarly journals Numerical Solution of Volterra-Fredholm Integral Equations with Hosoya Polynomials

2021 ◽  
Author(s):  
Ercan Çelik ◽  
Merve Geçmen
Keyword(s):  
Integral Equation ◽  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Programming Language ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Matlab Programming

In this study, Volterra-Fredholm integral equation is solved by Hosoya Polynomials. The solutions obtained with these methods were compared on the figure and table. And error analysis was done. Matlab programming language has been used to obtain conclusitions, tables and error analysis within a certain algorithm.

Numerical solution of two-dimensional first kind Fredholm integral equations by using linear Legendre wavelet

2016 ◽  
Vol 14 (01) ◽  
pp. 1650004 ◽  
Author(s):  
M. Tahami ◽  
A. Askari Hemmat ◽  
S. A. Yousefi
Keyword(s):  
Integral Equation ◽  
Tensor Product ◽  
Numerical Solution ◽  
Fredholm Integral Equation ◽  
Fredholm Integral Equations ◽  
Wavelet Basis ◽  
Two Dimensional ◽  
Legendre Wavelets ◽  
Numerical Examples ◽  
One Dimensional

In one-dimensional problems, the Legendre wavelets are good candidates for approximation. In this paper, we present a numerical method for solving two-dimensional first kind Fredholm integral equation. The method is based upon two-dimensional linear Legendre wavelet basis approximation. By applying tensor product of one-dimensional linear Legendre wavelet we construct a two-dimensional wavelet. Finally, we give some numerical examples.

scholarly journals High order iterative methods for matrix inversion and regularized solution of fredholm integral equation of first kind with noisy data

2018 ◽  
Vol 22 ◽  
pp. 01002
Author(s):  
Suzan Cival Buranay ◽  
Ovgu Cidar Iyikal
Keyword(s):  
Integral Equation ◽  
Iterative Methods ◽  
Fredholm Integral Equation ◽  
Recurrence Formula ◽  
Noisy Data ◽  
Matrix Inversion ◽  
High Order ◽  
The Given ◽  
High Order Iterative Methods ◽  
Regularized Solution

The motivation of the present work is to propose high order iterative methods with a recurrence formula for approximate matrix inversion and provide regularized solution of Fredholm integral equation of first kind with noisy data by an algorithm using the proposed methods. From the given family of methods of orders p = 7,11,15,19 are applied to solve problems of Fredholm integral equation of first kind. From the literature, iterative methods of same orders are used to solve the considered problems and numerical comparisons are shown through tables and figures.

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