Finite difference schemes for long-time integration

Authors:
Zigo Haras;Shlomo Ta'asan
Affiliations:
Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science and The Institute for Computer Applications in Science and Engineering, 76100 Rehovot, Israel;Department of Applied Mathematics and Computer Science, The Weizmann Institute of Science and The Institute for Computer Applications in Science and Engineering, 76100 Rehovot, Israel
Venue:
Journal of Computational Physics
Year:
1994

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Abstract

A general method for constructing finite difference schemes for longtime integration problems is presented. It is demonstrated for discretizations of first and second space derivatives; however, the approach is not limited to these cases. The schemes are constructed so as to minimize the global truncation error, taking into account the initial data. The resulting second-order compact schemes can be used for integration times fourfold or more longer than previously studied schemes with similar computational complexity. A similar approach was used to obtain improved integration schemes.