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On the treatment of time‐dependent boundary conditions in splitting methods for parabolic differential equations
Author(s) -
Sommeijer B. P.,
van der Houwen P. J.,
Verwer J. G.
Publication year - 1981
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620170304
Subject(s) - mathematics , boundary value problem , dirichlet boundary condition , mixed boundary condition , mathematical analysis , partial differential equation , cauchy boundary condition , free boundary problem , robin boundary condition , parabolic partial differential equation , singular boundary method , poincaré–steklov operator , elliptic partial differential equation , numerical partial differential equations , boundary element method , finite element method , physics , thermodynamics
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.