THE CONVERGENCE OF RICHARDSON'S FINITE-DIFFERENCE ANALOGUE FOR THE HEAT EQUATION.

Abstract

The theoretical convergence of Richardson's finite-difference analogue for the partial differential equation of heat flow is proved, and substantiating numerical results obtained from a high-speed digital computer are given. An analogy is drawn between the stability and convergence of Richardson's method in the discretization of partial differential equations and that of Milne's 'Method I' in ordinary differential equations. The numerical instability of Richardson's method is discussed. Concluding remarks disclose that although theoretical convergence is valid, numerical application of the method is limited due to the round-off error resulting from extremely small mesh sizes required for convergence.

Document Details

Document Type
Technical Report
Publication Date
May 01, 1969
Accession Number
AD0688660

Entities

People

  • Harold D. Eidson Jr

Organizations

  • University of Texas at Austin

Tags

DTIC Thesaurus Topics

  • Analogs
  • Computers
  • Convergence
  • Differential Equations
  • Digital Computers
  • Equations
  • Heat Transmission
  • Instability
  • Mathematical Analysis
  • Mathematics
  • Partial Differential Equations
  • Real Variables

Fields of Study

  • Mathematics

Readers

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