Explicit-implicit schemes for the numerical solution of nonlinear hyperbolic systems

Authors:
G. R. McGuire and J. Ll. Morris

Journal:
Math. Comp. **29** (1975), 407-424

MSC:
Primary 65M10

MathSciNet review:
0371085

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Abstract: A class of methods, comprising combinations of explicit and implicit methods, for solving systems of conservation laws in one space dimension is developed. The explicit methods of McGuire and Morris [5] are combined with the implicit methods of McGuire and Morris [11] in a manner similar to that for creating *Hopscotch* methods (Gourlay [13]). The stability properties of these *explicit-implicit* methods is investigated and the results of some numerical experiments are presented. Extensions of these methods to systems of conservation laws in two space dimensions are also briefly discussed.

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DOI:
https://doi.org/10.1090/S0025-5718-1975-0371085-X

Article copyright:
© Copyright 1975
American Mathematical Society