New three-step hybrid block methods for solving second order ordinary differential equations directly

Abstract EN

In developing the new methods, interpolation and collocation approach is employed where by power series approximate solution is used as a basis function while the second derivative of the approximated power series is considered as collocation polynomial.

The developed methods are then applied to solving some second order initial value problems of ordinary differential equations in order to examine the efficiency of the methods.

The generated numerical results reveal that the new methods performed better when comparison is made with existing methods.