The derivation and application of a four step Block Linear Multistep Method is hereby presented. To achieve this, Chebyshev polynomial was employed as basis function. Chebyshev polynomial was adopted as basis function based on its level of accuracy among other monomials in the interval [-1, 1]. Block method was adopted in this presentation based on its accuracy over the popular Predictor – Corrector method. The method under consideration gives solution at each grid point within the interval of integration. The method was arrived at by interpolating the polynomial equation and collocating the differential equation at some selected points. The order and error constant of the method were investigated likewise the consistency and zero stability which is one of the desirability property of linear multistep method were equally investigated. The method was applied to solve some second order ordinary differential equations and compare its level of accuracy with the analytical solution and equally compare its level of accuracy with some other existing methods.
Keywords: Block Method., Interpolation, chebyshev polynomial., collocation, corrector, predictor
