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Solving Multi‐Scale problems with heterogeneous finite difference methods
Author(s) -
Abdulle Assyr
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310555
Subject(s) - scale (ratio) , finite difference method , finite difference , differential equation , partial differential equation , mathematics , work (physics) , computer science , mathematical optimization , mathematical analysis , physics , quantum mechanics , thermodynamics
Multi‐scale differential equations are problems in which the variables can have different length scales. The direct numerical solution of differential equations with multiple scales is often difficult due to the work for resolving the smallest scale. We present here a strategy which allows the use of finite difference methods for the numerical solution of parabolic multi‐scale problems, based on a coupling of macroscopic and microscopic models for the original equation.