Mathematical Analysis and its Contemporary Applications

A modified Taylor-series for solving a Fredholm integral equation of the second kind

https://doi.org/10.30495/maca.2022.1956497.1056
Volume 4, Issue 4
Autumn 2022
Pages 39-48
Mathematical Analysis and its Contemporary Applications

Document Type : Original Article

Authors

Majid Amirfakhrian 1
Seyyed Mahmood Mirzaei 2

1 Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

2 Department of Mathematics, Gonbad Kavoos Branch, Islamic Azad University, Gonbad Kavoos, Iran

Abstract
In this paper, we propose a Taylor series expansion method for the second kind of Fredholm integral equation with smooth kernels. This method converts the integral equation into a linear equation system to reduce the amount of computation. We present convergence conditions. Finally, we show the efficiency of the method using some numerical examples.

Keywords

Taylor Series
Fredholm Integral Equation
Linear Equation System
  • Receive Date 12 April 2022
  • Revise Date 20 June 2022
  • Accept Date 01 August 2022

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