Modified Single-step Methods of Higher Order ofAccuracy for Stiff System of Ordinary Differential Equations

Abstract

In this paper, amodified single-step method is proposed to integrate stiff systems of ordinary differential equations. In order to obtain higher order A-stable methods, we have used second derivative of the solutions and imposedsome special sets of off-grid points in the formulation process of the algorithms. The consistency, convergence and order of accuracy of the algorithms were successfully established and in addition, the methods are found to be A-stable. The proposed methods which are self-starting were applied as simultaneous numerical integrators on non-overlapping intervals. In order to demonstrate the effectiveness of the proposed algorithms, some stiff systems of IVPs are considered and results obtained are compared with those from related schemes and from other methods in the literature.