Computation of an Accurate Implicit Block Method for Solving Third Order Ordinary Differential Equations Directly

摘要

This article discusses the derivation of block method with step-length of five for direct solution of initial value problems of third order ordinary differential equations (ODEs). This method is developed through interpolation and collocation of power series approximate solution. In addition, some basic properties of the method are also established. The developed method is then applied to solve some initial value problems of third order ODEs. The numerical results confirm the superiority of the new method over the existing methods in term of accuracy.