NEW UNIFORM ORDER EIGHT HYBRID THIRD DERIVATIVE BLOCK METHOD FOR SOLVING SECOND ORDER INITIAL VALUE PROBLEMS

Abstract

A number of authors have considered the solution of second order initial value problems (IVPs) and the adoption of block methods of order eight has been seen to be widely applied. However, these previously developed block methods have considered non-hybrid grid points. Hence, this article presents a new hybrid block method of order eight for solving second order IVPs with an improved level of accuracy when compared to previously existing order eight block methods in terms of error. The methodology employed involves a new generalized algorithm for developing the hybrid block method which is another novel contribution existing in this work. Hence, not only this article presents a new block method that can be adopted when solving real life problems modelled as second order IVPs, it also gives a more convenient algorithm for developing hybrid block methods.