THE CONVERGENCE OF RICHARDSON'S FINITE-DIFFERENCE ANALOGUE FOR THE HEAT EQUATION.
Interim technical rept. no. 20,
TEXAS UNIV AUSTIN COMPUTATION CENTER
Pagination or Media Count:
The theoretical convergence of Richardsons 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 Richardsons method in the discretization of partial differential equations and that of Milnes Method I in ordinary differential equations. The numerical instability of Richardsons 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.
- Numerical Mathematics