On the treatment of time-dependent boundary conditions in splitting methods for parabolic differential equations

✍ Scribed by B. P. Sommeijer; P. J. van der Houwen; J. G. Verwer

• Publisher: John Wiley and Sons
• Year: 1981
• Tongue: English
• Weight: 903 KB
• Volume: 17
• Category: Article
• ISSN: 0029-5981
• DOI: 10.1002/nme.1620170304

✦ Synopsis

Abstract

Splitting methods for time‐dependent partial differential equations usually exhibit a drop in accuracy if boundary conditions become time‐dependent. This phenomenon is investigated for a class of splitting methods for two‐space dimensional parabolic partial differential equations. A boundary‐value correction discussed in a paper by Fairweather and Mitchell for the Laplace equation with Dirichlet conditions, is generalized for a wide class of initial boundary‐value problems. A numerical comparison is made for the ADI method of Peaceman‐Rachford and the LOD method of Yanenko applied to problems with Dirichlet boundary conditions and non‐Dirichlet boundary conditions.