Convergence analysis for an iterative method for solving nonlinear parabolic systems

Mohammed Al-Refai

Research output: Contribution to journalArticlepeer-review


In a recent work, we have proposed a new iterative method based on the eigenfunction expansion to integrate nonlinear parabolic systems sequentially. In this paper, we prove that the method is convergent and give analytical rate for its convergence. Moreover, we determine the number of iterations needed to obtain a solution with a pre-determined level of accuracy. We then illustrate the convergence analysis with a problem in combustion theory. It is expected that the convergence analysis can be used for similar systems with time dependence.

Original languageEnglish
Pages (from-to)841-849
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - Dec 15 2006
Externally publishedYes


  • Combustion theory
  • Eigenfunction expansions
  • Galerkin method
  • Parabolic systems

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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