General Properties

Abstract

We begin this chapter with a concrete example. In this example we use the solutions of a difference scheme of rather low accuracy and achieve a more accurate approximate solution using the Richardson extrapolation with higher-order differences. We then extend these results to abstract problems: we first, formulate a sufficient condition for the existence of an expansion of the approximate solution in powers of the difference net mesh-size; then we prove that this expansion allows us to use either the Richardson extra­polation or higher-order difference corrections.