Numerical solutions of the Laplace's equation

Kamel Al-Khaled*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

This paper uses the sinc methods to construct a solution of the Laplace's equation using two solutions of the heat equation. A numerical approximation is obtained with an exponential accuracy. We also present a reliable algorithm of Adomian decomposition method to construct a numerical solution of the Laplace's equation in the form a rapidly convergence series and not at grid points. Numerical examples are given and comparisons are made to the sinc solution with the Adomian decomposition method. The comparison shows that the Adomian decomposition method is efficient and easy to use.

Original languageEnglish
Pages (from-to)1271-1283
Number of pages13
JournalApplied Mathematics and Computation
Volume170
Issue number2
DOIs
Publication statusPublished - Nov 15 2005

Keywords

  • Adomian decomposition method
  • Laplace equation
  • Numerical experiments
  • Sinc function

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

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