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Mathematics of Computation

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Hybrid difference methods for the initial boundary-value problem for hyperbolic equations

Author: Joseph Oliger
Journal: Math. Comp. 30 (1976), 724-738
MSC: Primary 65M10
MathSciNet review: 0428727
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Abstract: The use of lower order approximations in the neighborhood of boundaries coupled with higher order interior approximations is examined for the mixed initial boundary-value problem for hyperbolic partial differential equations. Uniform error can be maintained using smaller grid intervals with the lower order approximations near the boundaries. Stability results are presented for approximations to the initial boundary-value problem for the model equation $ {u_t} + c{u_x} = 0$ which are fourth order in space and second order in time in the interior and second order in both space and time near the boundaries. These results are generalized to a class of methods of this type for hyperbolic systems. Computational results are presented and comparisons are made with other methods.

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Article copyright: © Copyright 1976 American Mathematical Society