Stiffly stable continuous extension of second derivative linear multi-step methods with an off-step point for initial value problems in ordinary differential equations.

Abstract

In this paper, we introduce a continuous extension of second derivative linear multi-step methods with a hybrid point for the numerical solution of initial valued stiff ordinary differential equations. The continuous extension is based on the Gear's fixed step size backward differential methods [7]. The intervals of absolute stability of methods of step number k𕟯 are determined using the root locus plot. Numerical results of the methods solving a non-linearly stiff initial value problem in ordinary differential equations are compared with that from the state-of-the-art ordinary differential equations code of MATLAB discussed in Higham et al [9]. JONAMP Vol. 11 2007: pp. 175-190