Improved Second Order Methods for Parabolic Partial Differential Equations.

Abstract

Two new finite difference for the calculation of parabolic partial differential equations. The leading truncation error terms are derived and detailed comparisons are made with the errors associated with existing methods, namely the Crank-Nicolson method and Keller Box scheme. A number of examples of both linear and non-linear parabolic problems are computed with both the new and also the existing methods. The accuracy of all four methods are compared; based on the computational experiments and a comparison of the magnitudes of the leading truncation errors, it is concluded that the improved methods are to be preferred over the existing methods.

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Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1982
Accession Number
ADA122197

Entities

People

  • J. D. A. Walker
  • W. C. Lee

Organizations

  • Lehigh University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Boundaries
  • Boundary Layer
  • Boundary Layer Flow
  • Boundary Value Problems
  • Classification
  • Difference Equations
  • Differential Equations
  • Engineering
  • Equations
  • Flow
  • Layers
  • Mechanical Engineering
  • Partial Differential Equations
  • Scientific Research
  • Truncation

Fields of Study

  • Mathematics

Readers

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