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Numerical solutions of coupled systems of nonlinear elliptic equations
Author(s) -
Boglaev Igor
Publication year - 2012
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.20648
Subject(s) - monotone polygon , mathematics , nonlinear system , uniqueness , partial differential equation , domain decomposition methods , convergence (economics) , domain (mathematical analysis) , class (philosophy) , monotonic function , bernstein's theorem on monotone functions , mathematical analysis , strongly monotone , finite element method , computer science , physics , geometry , quantum mechanics , artificial intelligence , economics , thermodynamics , economic growth
This article deals with numerical solutions of a general class of coupled nonlinear elliptic equations. Using the method of upper and lower solutions, monotone sequences are constructed for difference schemes which approximate coupled systems of nonlinear elliptic equations. This monotone convergence leads to existence‐uniqueness theorems for solutions to problems with reaction functions of quasi‐monotone nondecreasing, quasi‐monotone nonincreasing and mixed quasi‐monotone types. A monotone domain decomposition algorithm which combines the monotone approach and an iterative domain decomposition method based on the Schwarz alternating, is proposed. An application to a reaction‐diffusion model in chemical engineering is given. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 621–640, 2012