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

Aves, M.A. and Griffiths, D.F. and Higham, D.J. (2000) Runge-Kutta solutions of a hyperbolic conservation law with source term. SIAM Journal on Scientific Computing, 22 (1). pp. 20-38. ISSN 1064-8275

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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.

Item type: Article
ID code: 179
Keywords: adaptivity, finite difference, nonnormality, spurious solution, steady state, computer science, applied mathematics, runge-kutta method, Electronic computers. Computer science, Mathematics
Subjects: Science > Mathematics > Electronic computers. Computer science
Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Related URLs:
    Depositing user: Ms Sarah Scott
    Date Deposited: 02 Mar 2006
    Last modified: 12 Mar 2012 10:35
    URI: http://strathprints.strath.ac.uk/id/eprint/179

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