On nonlocal monotone difference schemes for scalar conservation laws
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- by Bradley J. Lucier PDF
- Math. Comp. 47 (1986), 19-36 Request permission
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.References
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Additional Information
- © Copyright 1986 American Mathematical Society
- 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