Uniformly Order Eight Implicit Second Derivative Method for Solving Second-Order Stiff Ordinary Differential Equations ODEs

A one-step hybrid block method for initial value problems of general second order Ordinary Differential Equations has been studied in this paper. In the derivation of the method, power series is adopted as basis function to obtain the main continuous scheme through collocation and interpolations approach. Taylor method is also used together with new method to generate the non-overlapping numerical results. The new method is then applied to solve the system of second-order stiff ordinary differential equations and the accuracy is better when compared with the existing methods in terms of error.