A Graphical Search for Stiffly Stable Methods for Ordinary Differential Equations

Abstract

An interactive computer graphics program was used to search for stiffly stable methods of orders seven through fifteen. Previously, methods of orders up to six were known. Methods of orders seven and eight were found in this search. The evidence gathered for the class of methods which requires a minimum of previous values to be kept indicates that no stiffly stable methods of this type exist for orders eight through fifteen.