Numerical solution of quenching problems using mesh-dependent variable temporal steps

K. W. Liang, Ping Lin, R. C. E. Tan

    Research output: Contribution to journalArticle

    17 Citations (Scopus)

    Abstract

    In this paper, we introduce a new adaptive method for computing the numerical solutions of a class of quenching parabolic equations which exhibit a solution with one singularity. Our method systematically generates an irregular mesh with mesh-dependent temporal increments based on the solution behavior from which an implicit finite difference scheme associated with the irregular mesh is constructed. The convergence and stability of the finite difference scheme is analyzed for the solution before quenching. An equivalent linearized model is used to justify the stability of the method near quenching as well. A numerical example is provided to demonstrate the viability of the proposed method.
    Original languageEnglish
    Pages (from-to)791-800
    Number of pages10
    JournalApplied Numerical Mathematics
    Volume57
    Issue number5-7
    DOIs
    Publication statusPublished - May 2007

    Keywords

    • Nonlinear reaction-diffusion equations
    • Quenching problems
    • Singularity
    • Adaptive method
    • Irregular grids
    • Implicit finite difference scheme

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