NDLI: Block Monotone Iterative Method for Semilinear Parabolic Equations with Nonlinear Boundary Conditions

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Lu, Xin Pao, C. V.
Copyright Year	2010
Abstract	Two block monotone iterative schemes, called Jacobi and GaussSeidel monotone iterations, are presented for numerical solutions of a class of semilinear parabolic equations under nonlinear boundary conditions by the finite difference method. These iteration schemes extend the method for semilinear elliptic boundary value problems to parabolic equations, including a comparison result between them. It is shown that by using an upper solution and a lower solution as initial iterations each of the iterative schemes yields two sequences which converge monotonically from above and below, respectively, to a unique solution of the finite difference system. Some error estimates and a convergence theorem are given, and various sufficient conditions for the construction of upper and lower solutions are obtained. Numerical results are presented for some physical model problems, including some problems with known continuous solutions and two problems with L-shaped and trapezoidal domains.
Starting Page	4581
Ending Page	4606
Page Count	26
File Format	PDF
ISSN	00361429
DOI	10.1137/090748706
e-ISSN	10957170
Issue Number	6
Volume Number	47
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-02-17
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods numerical solutions finite difference systems convergence semilinear parabolic equations block monotone iterations Jacobi iterations and GaussSeidel iterations upper and lower solutions Reaction-diffusion equations nonlinear boundary conditions Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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