Development and L2-analysis of a single-step characteristics finite difference scheme of second order in time for convection-diffusion problems

Hirofumi Notsu, Hongxing Rui, Masahisa Tabata

    Research output: Contribution to journalArticlepeer-review

    5 Citations (Scopus)

    Abstract

    A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L2-theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.

    Original languageEnglish
    Pages (from-to)343-380
    Number of pages38
    JournalJournal of Algorithms and Computational Technology
    Volume7
    Issue number3
    DOIs
    Publication statusPublished - 2013 Sep 1

    Keywords

    • Discrete L-Analysis
    • Finite difference method
    • Second order in time
    • The method of characteristics

    ASJC Scopus subject areas

    • Numerical Analysis
    • Computational Mathematics
    • Applied Mathematics

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