Numerical comparison of methods for solving parabolic equations

Kamel Al-Khaled*, Dogan Kaya, Muhammad Aslam Noor

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Citations (Scopus)

Abstract

In this paper, we apply a new decomposition scheme to solve the linear heat equation. The approach is based on the choice of a suitable differential operator which may be ordinary or partial, linear or nonlinear, deterministic or stochastic. It does not require discretization and consequently of massive computation. In this scheme the solution is performed in the form of a convergent power series with easily computable components. This paper is particularly concerned with the Adomian decomposition method and the results obtained are compared to those obtained by a conventional finite-difference method and the Sinc method. The numerical results demonstrate that the new method is relatively accurate and easily implemented.

Original languageEnglish
Pages (from-to)735-743
Number of pages9
JournalApplied Mathematics and Computation
Volume157
Issue number3
DOIs
Publication statusPublished - Oct 15 2004

Keywords

  • A parabolic partial differential equation
  • Finite-difference method
  • Sinc functions
  • The Adomian decomposition method

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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