Accession Number : AD0688660

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

Descriptive Note : Interim technical rept. no. 20,

Corporate Author : TEXAS UNIV AUSTIN COMPUTATION CENTER

Personal Author(s) : Eidson,Harold D. , Jr

Report Date : MAY 1969

Pagination or Media Count : 113

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.

Descriptors :   (*CONDUCTION(HEAT TRANSFER), PARTIAL DIFFERENTIAL EQUATIONS), (*NUMERICAL INTEGRATION, NUMERICAL ANALYSIS), DIFFERENCE EQUATIONS, BOUNDARY VALUE PROBLEMS, CONVERGENCE, STABILITY, HEAT FLUX, THESES

Subject Categories : Numerical Mathematics
      Thermodynamics

Distribution Statement : APPROVED FOR PUBLIC RELEASE