One-step splitting methods for semi-discrete parabolic equations |
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Authors: | Prof Dr P J van der Houwen Dr J G Verwer |
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Affiliation: | 1. Mathematisch Centrum, 2de Boerhaavestraat 49, 1091 AL, Amsterdam, The Netherlands
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Abstract: | The main purpose of the paper is to discuss splitting methods for parabolic equations via the method of lines. Firstly, we deal with the formulation of these methods for autonomous semi-discrete equations $$\frac{{dy}}{{dt}} = f(y),{\rm E}f{\rm E}non - linear,$$ f satisfying a linear splitting relation \(f(y) = \sum\limits_{i = 1}^k {f_i (y)} \) . A class of one-step integration formulas is defined, which is shown to contain all known splitting methods, provided the functionsf i are defined appropriately. For a number of methods stability results are given. Secondly, attention is paid to alternating direction methods for problems with an arbitrary non-linear coupling between space derivatives. |
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