On the Error Analysis of a Continuous Implicit Hybrid One Step Method

Abstract

It is a known fact that in the application of a continuous linear multistep formula, the global error at a particular point is influenced by the accumulation of local truncation errors at each step from the initial point and thereby reduces the accuracy of the approximated result. Hence, by controlling the growth of local errors it is expected that the accuracy of the approximations should improve. In this paper therefore, a formula is derived for the bound on the local truncation error of a continuous implicit hybrid one step method for the solution of initial value problems of second order ordinary differential equations by means of the generalized Lagrange form of the Taylor’s remainder and the mean value theorem.