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Upwind finite difference schemes for linear conservation law with memory
Author(s) -
Lin Yanping
Publication year - 1994
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690100406
Subject(s) - mathematics , conservation law , finite difference , finite difference method , finite difference coefficient , upwind scheme , kernel (algebra) , class (philosophy) , mathematical analysis , finite element method , pure mathematics , computer science , mixed finite element method , physics , artificial intelligence , discretization , thermodynamics
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. © 1994 John Wiley & Sons, Inc.