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Mathematics of Computation

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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
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