Efficient Higher Order Single Step Methods for Parabolic Problems. Part I.

Abstract

Some efficient, high order methods are discussed for approximating the solution of an initial boundary value problem for a homogeneous parabolic equation with time dependent coefficients. The methods are based on Galerkin-type approximations in the spacial variables and single step methods in the time variable. The equations defining the time stepping procedure are solved only approximately however. A preconditioned iterative technique is used for this purpose. The resulting algorithm is shown to produce optimal order approximations using only the order of work required by the single step method applied to the parabolic problem with time independent coefficients. (Author)

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Document Details

Document Type
Technical Report
Publication Date
May 01, 1979
Accession Number
ADA070217

Entities

People

  • James H. Bramble
  • Peter H. Sammon

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Algorithms
  • Boundary Value Problems
  • Computations
  • Differential Equations
  • Eigenvalues
  • Equations
  • Errors
  • Iterations
  • Linear Systems
  • Mathematics
  • New York
  • Numerical Analysis
  • Partial Differential Equations
  • Polynomials
  • Rational Functions
  • Theorems
  • United States

Fields of Study

  • Mathematics

Readers

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