摘要：Solving Ordinary value problems (ODEs) numerically is an area that has drawn much considerationin latest literature and hence, the general object of this study. In this study, new hybrid block method isproposed using collocation and interpolation approach and then is employed to approximate third order initialvalue problems directly. Certain conditions of the block method established include it being of stepnumber k = 2 with two off-step points. This hybrid block method involves of mathematical expressions that willconcurrently supply results at the step and off-step points. Numerical properties which involve zero stability,order of the method, consistency and convergence are established. After that some third order initial valueproblems are considered and the new hybrid block method is employed to solve it numerically and comparisonwas made with existing methods in terms of error. The generated numerical results show superiority of the newmethod in terms of error. Therefore, this developed hybrid block method can be adopted a more appropriatenumerical approach to approximate the third order IVPs numerically.
关键词：two off step points;power series;third order differential equation;block method;Hybrid method;numerical
