On nonlocal monotone difference schemes for scalar conservation laws

Author:
Bradley J. Lucier

Journal:
Math. Comp. **47** (1986), 19-36

MSC:
Primary 65M10; Secondary 35L65

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842121-6

MathSciNet review:
842121

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Abstract: We provide error analyses for explicit, implicit, and semi-implicit monotone finite-difference schemes on uniform meshes with nonlocal numerical fluxes. We are motivated by finite-difference discretizations of certain long-wave (Sobolev) regularizations of the conservation laws that explicitly add a dispersive term as well as a nonlinear dissipative term. We also develop certain relationships between dispersion and stability in finite-difference schemes. Specifically, we find that discretization and explicit dispersion have identical effects on the amount of artificial dissipation necessary for stability.

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DOI:
https://doi.org/10.1090/S0025-5718-1986-0842121-6

Article copyright:
© Copyright 1986
American Mathematical Society