Order Ten Implicit One-Step Hybrid Block Method for The Solution of Stiff Second-order Ordinary Differential Equations

Y. Skwame, J. Sabo, P. Tumba, T. Y. kyagya

A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. The method is developed using interpolation and collocation techniques. The use of the power series approximate solution as an interpolation polynomial and its second derivative as a collocation equation is considered in deriving the method. Numerical analysis shows that the developed new method is consistent, convergent,   and order ten. The new method is then applied to solve the system of second-order ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error.