ANALYSIS OF FIXED-STEPSIZE METHODS

The unified theory developed by P. Henrici for one-step methods is extended to the more general case where the order of the system of difference equations can exceed the order of the system of ordinary differential equations. The analysis is applicable to every fixed-stepsize fixed-formula method known to the author. For many of these methods the concept of consistency is inadequate. A more appropriate concept, termed quasi-consistency, is introduced. The notion of optimal stability is simplified and extended for the special case of step-by-step methods for ordinary differential equations.