On a new method for finding numerical solutions to integro-differential equations based on Legendre multi-wavelets collocation

Imran Khan, Muhammad Asif, Rohul Amin, Qasem Al-Mdallal, Fahd Jarad

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

In this article, a wavelet collocation method based on linear Legendre multi-wavelets is proposed for the numerical solution of the first as well as higher orders Fredholm, Volterra and Volterra–Fredholm integro-differential equations. The presented numerical method has the capability to tackle the solutions of both linear and nonlinear problems of these model equations. In order to endorse accuracy and efficiency of the method, it is tested on various numerical problems from literature with the aid of maximum absolute errors and rates of convergence. L norms are used to compare the numerical results with other available methods such as Multi-Scale-Galerkin's method, Haar wavelet collocation method and Meshless method from literature. The comparability of the presented method with other existing numerical methods demonstrates superior efficiency and accuracy.

Original languageEnglish
Pages (from-to)3037-3049
Number of pages13
JournalAlexandria Engineering Journal
Volume61
Issue number4
DOIs
Publication statusPublished - Apr 2022

Keywords

  • Fredholm integro-differential equations of first and higher-orders
  • Linear Legendre multi-wavelets
  • Volterra integro-differential equations of first and higher-orders

ASJC Scopus subject areas

  • Engineering(all)

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