A Self-Starting Block Methods (SSBMs) for the Solution of Ordinary Differential Equations

Abstract

In this paper, self-starting block numerical methods for the solution of stiff initial value problems ordinary differential equations were developed. The Backward Differentiation Formulas and Generalized Backward Differentiation Formulas are used in the derivations. The E-transformation is applied to the triples and self-starting methods are obtained. The numerical implementation of the methods on ordinary differential equations are reported to show the effectiveness and efficiency of the methods. The computational of convergence of absolute stability and consistent tends to the theoretical order as h tends to zero.