Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations. (18th January 2017) - Alkasassbeh, Mohammad; Omar, Zurni
Abstract : A new one-step block method with generalized three hybrid points for solving initial value problems of second-order ordinary differential equations directly is proposed. In deriving this method, a power series approximate function is interpolated at x n, x n + r while its second and third derivatives are collocated at all points x n, x n + r, x n + s, x n + t, x n + 1 in the given interval. The proposed method is then tested on initial value problems of second-order ordinary differential equations solved by other methods previously. The numerical results confirm the superiority of the new method to the existing methods in terms of accuracy.