A comparison of Numerical Solutions for Linear Fredholm Integral Equation of the Second Kind

The aim of this paper, we offereda new numerical methodwhich is Touchard Polynomials (T-Ps) for solving Linear Fredholm Integral Equation of the Second Kind (LFIE2-K), to find approximating Numerical Solution (N-S). At the beginning, we demonstrate (T-Ps) andconstruct the operational matrix which is...

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Published in:Journal of physics. Conference series 2019-07, Vol.1279 (1), p.12067
Main Authors: Talab Abdullah, Jalil, Hussein Shuaa Al-Taie, Ali
Format: Article
Language:English
Subjects:
Algorithms
Exact solutions
Fredholm equations
Fredholm Integral Equation
Integral equations
Matrix representation
Numerical methods
Physics
Polynomials
Touchard&Bernstein polynomials
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Hussein Shuaa Al-Taie, Ali
description The aim of this paper, we offereda new numerical methodwhich is Touchard Polynomials (T-Ps) for solving Linear Fredholm Integral Equation of the Second Kind (LFIE2-K), to find approximating Numerical Solution (N-S). At the beginning, we demonstrate (T-Ps) andconstruct the operational matrix which is a matrix representation for solution. The algorithm and someexamples are given; comparing the numerical results of proposed method with the numerical results of the other numerical method which is Bernstein Polynomials (B-Ps).Wewill show the high resolution of results by proposed method.The comparison between the Exact Solution(E-S) and the results of two methods are given by calculating absolute value of error and the Least Square Error (L.S.E).The results are calculated in Matlabcode.
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subjects Algorithms
Exact solutions
Fredholm equations
Fredholm Integral Equation
Integral equations
Matrix representation
Numerical methods
Physics
Polynomials
Touchard&Bernstein polynomials
title A comparison of Numerical Solutions for Linear Fredholm Integral Equation of the Second Kind
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