Numerical Solution of Semi-Linear Elliptic Problems on Unbounded Domains.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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This document presents the derivation and implementation of asymptotic boundary conditions at artificial boundaries for semi-linear elliptic boundary value problems on semi-infinite cylindrical domains. A general theory developed by the authors in a previous work is applied to establish the existence of exact boundary conditions and to obtain useful approximations to them. These are based on the Laplace transform solution of the linearized problem at infinity. The authors discuss the incorporation of these conditions in a finite difference scheme and present the results of a numerical experiment the solution of the Bratu problem in a two dimensional stepped channel. They also examine certain problems concerning the existence of solutions on infinite domains.
- Numerical Mathematics