J.G. Verwer

One-Step Splitting Methods for Semi-Discrete Parabolic Equations

AbstractThe 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 equationsn

On stabilized integration for time-dependent PDEs

frac{{dy}}{{dt}} = f(y),{rm E}f{rm E}non - linear,

A numerical study of mixed parabolic---gradient systems

nf satisfying a linear splitting relationn

Time Integration Methods

f(y) = sumlimits_{i = 1}^k {f_i (y)}

Time integration of Maxwell's equations

n. A class of one-step integration formulas is defined, which is shown to contain all known splitting methods, provided the functionsfi 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.ZusammenfassungIn dem Artikel werden speziell die Split-Methoden für parabolische Gleichungen mittels der Linienmethode besprochen. Bei diesen Methoden behandeln wir zuerst die Formulierung für autonome semi-diskrete Gleichungenn