A Study of High Accuracy High Derivative Formulas for the Numerical Integration of Stiff Equations

Abstract

<p>Different methods have been designed to solve systems of ordinary differential equations which avoid the restriction on step size imposed by the stability requirements alone and may be severe when the conventional numerical methods are used in solving stiff systems. This area requires further study which will lead to the development of new methods which are suitable for solving stiff equations and at the same time have high order of accuracy.</p> <p>In this investigation, classes of multistep formulas using high derivations are studied and searched for the existence of high order stiffly stable formulas, and of better stability region formulas. Stiffly stable formulas of order as to 14 were found in this search and better stability regions have been obtained by varying the choice of arbitrary coefficients to control the stability characteristics.</p>