Higher Derivative Direct Block Methods for Fourth-order Initial Value Problems of Ordinary Differential Equations

Direct Block Methods for solving fourth-order Initial Value Problems (IVPs) are presented. The derivation of the methods is achieved by applying the technique of inter- polation and collocation to a power series polynomial, which is considered an approximate solution to the problems. Higher derivative terms are introduced to improve the order of accuracy of the methods. Details of the block methods are presented, showing that the methods are zero stable, consistent and convergent. Some scalar and vector problems of IVPs are presented to illustrate the accuracy of the proposed approach, providing a com- prehensive comparison with other methods in the literature.