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

## 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 |
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ID code: | 179 |

Keywords: | adaptivity, finite difference, nonnormality, spurious solution, steady state, computer science, applied mathematics, runge-kutta method, Electronic computers. Computer science, Mathematics, Computational Mathematics, Applied 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: | 04 Sep 2014 10:10 |

URI: | http://strathprints.strath.ac.uk/id/eprint/179 |

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