Runge-Kutta solutions of a hyperbolic conservation law with source term

Mark A. Aves, David Griffiths, Desmond. J. Higham

    Research output: Contribution to journalArticle

    3 Citations (Scopus)
    110 Downloads (Pure)

    Abstract

    Spurious long-term solutions of a finite-difference method for a hyperbolic conservation law with a general nonlinear source term are studied. Results are contrasted with those that have been established for nonlinear ordinary differential equations. Various types of spurious behavior are examined, including spatially uniform equilibria that exist for arbitrarily small time-steps, nonsmooth steady states with profiles that jump between fixed levels, and solutions with oscillations that arise from nonnormality and exist only in finite precision arithmetic. It appears that spurious behavior is associated in general with insufficient spatial resolution. The potential for curbing spuriosity by using adaptivity in space or time is also considered.
    Original languageEnglish
    Pages (from-to)20-38
    Number of pages19
    JournalSIAM Journal on Scientific Computing
    Volume22
    Issue number1
    DOIs
    Publication statusPublished - 2000

    Fingerprint

    Hyperbolic Conservation Laws
    Runge-Kutta
    Source Terms
    Finite difference method
    Ordinary differential equations
    Conservation
    Nonlinear Source
    Non-normality
    Adaptivity
    Nonlinear Ordinary Differential Equations
    Spatial Resolution
    Difference Method
    Finite Difference
    Jump
    Oscillation
    Profile

    Keywords

    • Adaptivity
    • Finite differences
    • Nonnormality
    • Spurious solution
    • Steady state

    Cite this

    Aves, Mark A. ; Griffiths, David ; Higham, Desmond. J. / Runge-Kutta solutions of a hyperbolic conservation law with source term. In: SIAM Journal on Scientific Computing. 2000 ; Vol. 22, No. 1. pp. 20-38.
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    Runge-Kutta solutions of a hyperbolic conservation law with source term. / Aves, Mark A.; Griffiths, David; Higham, Desmond. J.

    In: SIAM Journal on Scientific Computing, Vol. 22, No. 1, 2000, p. 20-38.

    Research output: Contribution to journalArticle

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    T1 - Runge-Kutta solutions of a hyperbolic conservation law with source term

    AU - Aves, Mark A.

    AU - Griffiths, David

    AU - Higham, Desmond. J.

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    KW - Nonnormality

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    KW - Steady state

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