The importance of numerical solution to differential equations cannot be overemphasized. It has been observed that the analytic method of solution to some differential equation often became laborious and practicably impossible. In order to circumvent this problem, then the introduction of an approximate solution became inevitable. This paper focuses on the derivation and application of an appropriate continuous linear multistep method in a block form in solving first order ordinary differential equations by collocating at some selected off grid points and interpolating at only one grid point. To achieve this, Chebyshev polynomial is used as basis function. Some basic properties of Multistep methods were critically examined such as order, consistency, zero stability and region of absolute stability and the level of accuracy of the method was equally compared with an existing method and was found out to performs better that the method compared with.
Keywords: Interpolation, chebyshev polynomial., collocation, consistency, multistep
