Convergence of numerical schemes for the solution of partial integro-differential equations used in heat transfer

Kamel Al-Khaled*, Amer Darweesh, Maha H. Yousef

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

Integro-differential equations play an important role in may physical phenomena. For instance, it appears in fields like fluid dynamics, biological models and chemical kinetics. One of the most important physical applications is the heat transfer in heterogeneous materials, where physician are looking for efficient methods to solve their modeled equations. The difficulty of solving integro-differential equations analytically made mathematician to search about efficient methods to find an approximate solution. The present article is designed to supply numerical solution of a parabolic Volterra integro-differential equation under initial and boundary conditions. We have made an attempt to develop a numerical solution via the use of Sinc-Galerkin method, the convergence analysis via the use of fixed point theory has been discussed, and showed to be of exponential order. For comparison purposes, we approximate the solution of integro-differential equation using Adomian decomposition method. Sometimes, the Adomian decomposition method is a highly efficient technique used to approximate analytical solution of differential equations, applicability of Adomian decomposition method to partial integro-differential equations has not been studied in details previously in the literatures. In addition, we present numerical examples and comparisons to support the validity of these proposed methods.

Original languageEnglish
Pages (from-to)657-675
Number of pages19
JournalJournal of Applied Mathematics and Computing
Volume61
Issue number1-2
DOIs
Publication statusPublished - Oct 1 2019
Externally publishedYes

Keywords

  • Adomian decomposition method
  • Fixed point theory
  • Integro-differential equation
  • Sinc-Galerkin method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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