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