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

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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.

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