The solution of non-linear diffusion equation under stochastic nonhomogeneity using symbolic WHEP and Pickard algorithms

Magdy A. El-Tawil, Noha Almulla

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

1 Scopus citations

Abstract

In this paper, a nonlinear diffusion equation is studied under stochastic nonhomogeneity through homogeneous boundary conditions. The analytical solution for the linear case is obtained using the eigenfunction expansion. The Pickard approximation method is used to introduce a first order approximate solution for the nonlinear case. The WHEP technique is also used to obtain approximate solution under different orders and different corrections. Using Mathematica-5, the solution algorithm is operated through first order approximation. The method of solution is illustrated through case studies and figures.

Original languageEnglish (US)
Title of host publicationTransactions on Computational Science VII
EditorsMarina L. Gavrilova, C.J. Kenneth Tan
Pages75-100
Number of pages26
DOIs
StatePublished - May 13 2010

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5890 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Keywords

  • Eigenfunction expansion
  • Nonlinear diffusion equation
  • Pickard approximation
  • WHEP technique

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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