A New Single Step Hybrid Block Algorithm for Solving Fourth Order Ordinary Differential Equations Directly

In this paper, a one-step hybrid block method with generalized three off -step points for solving general fourth order ordinary differential equations is developed using power series of order eight as a basis function. The technique employed for the derivation of this method are to interpolate the power series at xn and all off-step points and to collocate the fourth derivative of the basis function at all points in the selected interval. The method derived is proven to be zero stable, consistent and then convergent. The performance of the method is tested by solving linear and non-linear fourth order initial value problems.