Numerical Solution of Semi-Linear Elliptic Problems on Unbounded Domains.

Abstract

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.

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Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1984
Accession Number
ADA149559

Entities

People

  • H. B. Keller
  • T. M. Hagstrom

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Asymptotic Series
  • Boundary Value Problems
  • Computations
  • Contracts
  • Differential Equations
  • Eigenvalues
  • Equations
  • Flow
  • Fluid Flow
  • Formulas (Mathematics)
  • Geometry
  • Mathematics
  • Theorems
  • Two Dimensional
  • United States

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)