Abstract

In this paper, we introduce multivalue multistep implicit methods with second derivative evaluations for continuous solution of stiff systems. The proposed methods are derived by introducing intermediate off-step points in between the familiar step-points suitable for continuous solution of stiff systems. Considerable gain in efficiency, accuracy and stability are achieved by the modification of the methods to contain second derivative evaluations. Plots of the stability regions in the complex plane show that they are stable, convergent, with large regions of absolute stability. A global error estimation of the approximate solution is described. The new methods show remarkable performance over a broad class of linear and nonlinear stiff systems, due to their high order of accuracy and stiffly accurate characteristic properties. The results of preliminary experiments are presented which are in better agreement with the exact solutions.

Key words: Block method, Continuous scheme, Multistep method, Second derivative method, Stiff system