Derivation of the Adomian decomposition method using the homotopy analysis method

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101 Citations (Scopus)

Abstract

Adomian decomposition method has been used intensively to solve nonlinear boundary and initial value problems. It has been proved to be very efficient in generating series solutions of the problem under consideration under the assumption that such series solution exits. However, very little has been done to address the mathematical foundation of the method and its error analysis. In this article the mathematical derivation of the method using the homotopy analysis method is presented. In addition, an error analysis is addressed as well as the convergence criteria.

Original languageEnglish
Pages (from-to)6-14
Number of pages9
JournalApplied Mathematics and Computation
Volume190
Issue number1
DOIs
Publication statusPublished - Jul 1 2007

Keywords

  • Adomian decomposition method
  • Convergence criteria
  • Error analysis
  • Homotopy analysis method

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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