A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method-Reference-Cited by-同舟云学术

A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method

Published:2021-09-03 Issue: Volume:2021 Page:1-11
ISSN:1563-5147
Container-title:Mathematical Problems in Engineering
language:en
Short-container-title:Mathematical Problems in Engineering

Author:

Khidir Ahmed A.¹²^ORCID

Affiliation:

1. Faculty of Technology of Mathematical Sciences and Statistics, Alneelain University, P.O. Box 12702, Khartoum, Sudan

2. Department of Mathematics, Faculty of Sciences, University of Tabuk, P.O. Box 741, Tabuk, Saudi Arabia

Abstract

In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. The application of the proposed method leads Volterra integral equation to a system of algebraic equations that are easy to solve. Some examples are presented and compared with some methods in the literature to illustrate the ability of this technique. The results demonstrate that the new method is more efficient, convergent, and accurate to the exact solution.

Publisher

Hindawi Limited

Subject

General Engineering,General Mathematics

Link

http://downloads.hindawi.com/journals/mpe/2021/9230714.pdf

Reference29 articles.

1. A comparison study between the modified decomposition method and the traditional methods for solving nonlinear integral equations

2. Linear and Nonlinear Integral Equations

3. Volterra integral equations: an introduction to theory and applications;H. Brunner,2017

4. A new method based on Haar wavelet for the numerical solution of two-dimensional nonlinear integral equations

Cited by 4 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. A collocation method based on roots of Chebyshev polynomial for solving Volterra integral equations of the second kind;Applied Mathematics Letters;2023-12

2. An efficient numerical algorithm for solving nonlinear Volterra integral equations in the reproducing kernel space;Journal of Applied Mathematics and Computing;2023-05-24

3. The Spectral Adomian Decomposition Method for the Solution of MHD Jeffery–Hamel Problem;Mathematical Problems in Engineering;2023-02-04

4. Approximation Technique for Solving Linear Volterra Integro-Differential Equations with Boundary Conditions;Abstract and Applied Analysis;2022-04-12