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An analysis of alternating‐direction methods for parabolic equations
Author(s) -
Celia Michael A.,
Plnder George F.
Publication year - 1985
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.1690010107
Subject(s) - mathematics , alternating direction implicit method , discretization , mathematical analysis , finite element method , parabolic partial differential equation , partial differential equation , collocation (remote sensing) , matrix (chemical analysis) , space (punctuation) , finite difference method , physics , materials science , composite material , thermodynamics , linguistics , philosophy , remote sensing , geology
Alternating‐direction solution procedures for parabolic partial differential equations can be developed using finite‐difference, finite‐element, and collocation approximations in space. Each of these methods derives from a common alternating‐direction formulation. Furthermore, each method leads to an O [(Δ t ) 2 ] error which is in addition to the discretization error associated with standard multidimensional solutions. However, when dealing with equations having spatially varying coefficients, some alternating‐direction formulations lead to yet other errors which are O (Δ t ). These latter errors, and thus the accuracy of the method, depend on the structure of the mass matrix associated with the approximating method.