Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations

Abstract EN

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 {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+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.