Exact Boundary Conditions at an Artificial Boundary for Partial Differential Equations in Cylinders.

Abstract

The numerical solution of partial differential equations in unbounded domains requires a finite computational domain. Often one obtains a finite domain by introducing an artificial boundary and imposing boundary conditions there. This paper derives exact boundary conditions at an artificial boundary for partial differential equations in cylinders. An abstract theory is developed to analyze the general linear problem. Solvability requirements and estimates of the solution of the resulting finite problem are obtained by use of the notions of exponential and ordinary dichotomies. Useful representations of the boundary conditions are derived using separation of variables for problems with constant tails. The constant tail results are extended to problems whose coefficients obtain limits at infinity by use of an abstract perturbation theory. The perturbation theory approach is also applied to a class of nonlinear problems. General asymptotic formulas for the boundary conditions are derived and displayed in detail. (Author)

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1984
Accession Number
ADA139310

Entities

People

  • H. B. Keller
  • T. Hagstrom

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Energy and Power Technologies
  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Boundary Value Problems
  • Cauchy Problem
  • Difference Equations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Fluid Flow
  • Formulas (Mathematics)
  • Mathematics
  • Numerical Analysis
  • Partial Differential Equations
  • Perturbation Theory
  • Perturbations
  • Theorems
  • United States

Fields of Study

  • Mathematics

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  • Calculus or Mathematical Analysis