Numerical Approximation of a Cauchy Problem for a Parabolic Partial Differential Equation.

Abstract

In many physical problems in heat conduction, it is impossible to obtain an initial temperature distribution within a material. In many of these cases, in order to obtain approximations of the temperature within the body, one must rely entirely upon data which can be measured at the boundary. An additional problem is that these boundary data are only accurate to within some prescribed measurement errors. The purpose of this paper is to define a procedure for numerically approximating the solution of one such heat flow problem and to present explicit error estimates for the numerical procedure. A priori error estimates are presented when the data are known only approximately.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1978
Accession Number
ADA064041

Entities

People

  • Richard E. Ewing
  • Richard S. Falk

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Boundaries
  • Boundary Value Problems
  • Cauchy Problem
  • Difference Equations
  • Differential Equations
  • Equations
  • Formulas (Mathematics)
  • Heat Transmission
  • Inequalities
  • Materials
  • Mathematics
  • Measurement
  • Numerical Analysis
  • Partial Differential Equations
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Computational Modeling and Simulation
  • Fluid Dynamics.