Contractivity of locally one-dimensional splitting methods

J. G. Verwer
1984 Numerische Mathematik  
The aim of this paper is to study contractivity properties of two locally one-dimensional splitting methods for non-linear, multi-space dimensional parabolic partial differential equations. The term contractivity means that perturbations shall not propagate in the course of the time integration process. By relating the locally one-dimensional methods with contractive integration formulas for ordinary differential systems it can be shown that the splitting methods define contractive numerical
more » ... utions for a large class of non-linear parabolic problems without restrictions on the size of the time step.
doi:10.1007/bf01410109 fatcat:q7o3hjeu2fftldbo4fxibsa524