On nonlocal monotone difference schemes for scalar conservation laws

Lucier, Bradley J.

doi:10.1090/S0025-5718-1986-0842121-6

On nonlocal monotone difference schemes for scalar conservation laws
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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.

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