ONE-STEP SPLITTING METHODS FOR SEMI-DISCRETE PARABOLIC EQUATIONS

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 {Mathematical expression}f satisfying a linear splitting relation {Mathematical expression}. A class of one-step integration formulas is defined, which is shown to contain all known splitting methods, provided the functions fi 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. © 1979 Springer-Verlag.