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.
|Number of pages||15|
|Journal||Numerical Methods for Partial Differential Equations|
|Publication status||Published - 1 Jan 1994|
ASJC Scopus subject areas
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics