Generalised Four Step Adams-Moulton Second Derivative Method for the Solution Stiff Ordinary Differential Equations

Abstract

A uniform order ten second derivative block method is presented for solving stiff ordinary differential equations. The proposed method was derived by using the approach of collocation and interpolation of four step Adams-Moulton method. Four individual schemes that made up the block method are obtained at step number, k = 4. The stability properties of the new method have been ascertained and it has shown to be consistent, zero–stable and A–stable. The solutions of two problems have been computed and compared with the corresponding exact and other existing solutions. Solutions are presented on graphs and the associated absolute errors are compared with some existing solution-errors in tables.