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Construction of nonstandard finite difference schemes for $1{1\over 2}$ space‐dimension‐coupled PDEs
Author(s) -
Mickens Ronald E.,
Jordan P.M.
Publication year - 2007
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.20172
Subject(s) - mathematics , dimension (graph theory) , partial differential equation , space (punctuation) , partial derivative , construct (python library) , finite difference , mathematical analysis , pure mathematics , computer science , programming language , operating system
Two coupled PDEs, where one has a diffusion term and the other does not, are defined to be $1{1\over 2}$ space‐dimension systems. We show how to construct nonstandard finite difference schemes for such systems and demonstrate that they are positivity‐preserving. These methods also allow the calculation of an explicit functional relationships between the time and space step‐sizes. The case of water flowing through fractured bedrock is used to illustrate our procedure. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007