Upwind finite difference schemes for linear conservation law with memory

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Abstract

In this article we consider upwind finite difference schemes for a class of linear conservation laws with memory. Assuming the positivity of the kernel, it is proved by using the energy estimates that the upwind finite difference scheme, explicit or implicit, is stable and convergent to the real solution. The numerical results of some examples, including Burger's equation with memory, are reported; the effect of memory is also discussed based on the numerical results.
Original languageEnglish
Pages (from-to)475-489
Number of pages15
JournalNumerical Methods for Partial Differential Equations
Volume10
Issue number4
DOIs
Publication statusPublished - 1 Jan 1994
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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