Numerical approximation of a cauchy problem for a parabolic partial differential equation

Richard E. Ewing, Richard S. Falk

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

A procedure for the numerical approximation of the Cauchy problem for the following linear parabolic partial differential equation is defined ut-((x)ux)x+q(x)u=0, 0<x<1, 0<tT, u(0, t)=f1(t, 0<tT;u(1, t)=f2(t), 0<tT;p(0)ux(0.t)=g(t), 0<t0tT;u(x, t)M, 0The procedure involves Galerkin-type numerical methods for related parabolic initial boundary-value problems and a linear programming problem. Explicit a priori error estimates are presented for the entire discrete procedure when the data fx, f2, and g are known only approximately.

Original languageEnglish (US)
Pages (from-to)1125-1144
Number of pages20
JournalMathematics of Computation
Volume33
Issue number148
DOIs
StatePublished - Oct 1979

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Cauchy problem
  • Error estimates
  • Improperly posed problem

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