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A family of fourth-order parallel splitting methods for parabolic partial differential equations

✍ Scribed by M. S. A. Taj; E. H. Twizell

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 149 KB
Volume: 13
Category: Article
ISSN: 0749-159X
DOI: 10.1002/(sici)1098-2426(199707)13:4<357::aid-num4>3.0.co;2-k

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✦ Synopsis

A family of numerical methods which are L-stable, fourth-order accurate in space and time, and do not require the use of complex arithmetic is developed for solving second-order linear parabolic partial differential equations. In these methods, second-order spatial derivatives are approximated by fourth-order finitedifference approximations, and the matrix exponential function is approximated by a rational approximation consisting of three parameters. Parallel algorithms are developed and tested on the one-dimensional heat equation, with constant coefficients, subject to homogeneous and time-dependent boundary conditions. These methods are also extended to two-and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions.

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