On the consistency and convergence of classical Richardson extrapolation as applied to explicit one-step methods

Abstract

The consistency of the classical Richardson extrapolation (CRE), a simple and robust computational device, is analysed for the case where the underlying method is an explicit one-step numerical method for ordinary differential equations with order of consistency one or two. It is shown in the classical framework that the CRE increases the order of consistency by one. The convergence of the method is proved by the assumption that the time-stepping operator of the base method has the Lipschitz property in its second argument.

Keywords

• consistency
• convergence
• explicit method
• Richardson extrapolation
• Taylor series expansion