Predictor-corrector block method of order seven for solving third order ordinary differential equations

Abstract

This paper discusses the development of a new predictor-corrector block method of order seven for direct solution of third order initial value problems. The approach adopted in the derivation of the new numerical method is interpolation and collocation whereby power series approximate solution is used as an interpolation polynomial and its highest derivative is considered as a collocation equation. The properties of the new developed method such as zero-stability, order, error constant, consistency and convergence are investigated. The new method was applied to some third order ordinary differential equations in order to examine its accuracy and the results produced are found better when compared with the existing methods in terms of error.