Newly developed single-step block method for numerical solution of fourth order ordinary differential equations

Abstract

This paper focuses on the development of a new block method for solving fourth order initial value problems of ordinary differential equations. Applying Chebyshev polynomial as a basis function, the method was developed using interpolation and collocation approaches. The convergence property of the method was established with zero-stability and consistency. Comparison was made with existing method, and the newly developed method compares favourably well.