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Generalized alternating‐direction collocation methods for parabolic equations. III. Nonrectangular domains
Author(s) -
Celia Michael A.,
Pinder George F.
Publication year - 1990
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.1690060304
Subject(s) - mathematics , collocation (remote sensing) , collocation method , partial differential equation , parabolic partial differential equation , mathematical analysis , alternating direction implicit method , orthogonal collocation , parabolic cylindrical coordinates , differential equation , ordinary differential equation , finite difference method , parabolic cylinder function , computer science , machine learning
The alternating‐direction collocation (ADC) method is an efficient numerical approximation technique for the solution of parabolic partial differential equations. However, to date the ADC method has only been developed for rectangular discretizations. With judicious combination of isoparametric coordinate transformations and an extended ADC approach, the ADC method can be formulated on general nonrectangular domains. This extends the applicability of the ADC method by allowing it to be employed on domains of more general geometry.