Two-Step Hybrid Block Method for Solving Second Order Initial Value Problem of Ordinary Differential Equations

A new zero-stable two-step hybrid block method for solving second order initial value problems of ordinary differential equations directly is derived and proposed. In the derivation of the method, the assumed power series solution is interpolated at the initial and the hybrid points while its second ordered derivative is collocated at all the nodal and selected off-step points in the interval of consideration. The relevant properties of the method were examined and the method was found to be zero-stable, consistent and convergent. A comparison of the results by the method with the exact solutions and other results in literature shows that the method is accurate, simple and effective in solving the class of problems considered.