MOHAMMED, U.AJINUHI, J. O.JIMOH, OMANANYI RAZAQDAUDA, A. A.AKINTUBUBO, B. G.2025-04-222019-09-150748-4710http://repository.futminna.edu.ng:4000/handle/123456789/887In 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.enArticle