A note on the operator compact implicit method for the wave equation

Authors:
Melvyn Ciment and Stephen H. Leventhal

Journal:
Math. Comp. **32** (1978), 143-147

MSC:
Primary 65M05

MathSciNet review:
0483507

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Abstract: In a previous paper a fourth order *compact implicit scheme* was presented for the second order wave equation. A very efficient factorization technique was developed when only second order terms were present. In this note we implement the *operator compact implicit* spatial discretization method for the second order wave equation when first order terms are present. The resulting algorithm is completely analogous to the compact implicit algorithm when lower order terms were not present. For this more general operator compact implicit spatial approximation the same factorization as in our previous paper is developed.

**[1]**Melvyn Ciment and Stephen H. Leventhal,*Higher order compact implicit schemes for the wave equation*, Math. Comp.**29**(1975), no. 132, 985–994. MR**0416049**, 10.1090/S0025-5718-1975-0416049-2**[2]**Melvyn Ciment, Stephen H. Leventhal, and Bernard C. Weinberg,*The operator compact implicit method for parabolic equations*, J. Comput. Phys.**28**(1978), no. 2, 135–166. MR**505588**, 10.1016/0021-9991(78)90031-1**[3]**Richard S. Hirsh,*Higher order accurate difference solutions of fluid mechanics problems by a compact differencing technique*, J. Computational Phys.**19**(1975), no. 1, 90–109. MR**0400909****[4]**Carl de Boor (ed.),*Mathematical aspects of finite elements in partial differential equations*, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1974. Publication No. 33 of the Mathematics Research Center, The University of Wisconsin-Madison. MR**0349031**

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DOI:
https://doi.org/10.1090/S0025-5718-1978-0483507-7

Keywords:
Wave equation,
higher order difference method

Article copyright:
© Copyright 1978
American Mathematical Society