Application of richardson extrapolation to linear functional equations with mildly smooth solutions

Abstract

Sufficient conditions are given under which discretization errors for numerical methods applied to linear functional equations possess power series expansions of a special form. The conditions are quite general and are applicable, for example, to problems whose solutions are only mildly smooth. It is shown that Richardson extrapolation can be applied to numerical methods that possess such error expansions. Several numerical examples are presented that illustrate application of the conditions.

Keywords:

• Extrapolation
• numerical analysis
• difference methods
• error analysis mathematics of computation

C.R.Categories:

• G.1.0
• G.1.1