CHEBYSHEV COLLOCATION APPROACH FOR CONTINUOUS FOUR-STEP HYBRID BACKWARD DIFFERENCE FORMULA FOR STIFF SYSTEM

Abstract

In this paper, we developed an implicit continuous four-step hybrid backward difference formulae for the direct solution of stiff system. For this purpose, the Chebyshev polynomial was employed as the basis function for the development of schemes in a collocation and interpolation techniques. The schemes were analysed using appropriate existing theorem to investigate their stability, consistency, convergence and the investigation shows that the developed schemes are consistent, zero-stable and hence convergent. The methods were implemented on test problem from the literatures to show the accuracy and effectiveness of the scheme.