An optimal 6-step implicit linear multistep method for initial value problems

Abstract

In this paper, we employ Taylor series expansion to develop a 6-step implicit linear multistep method of optimal order, for solving initial value problems. By assigning a suitable value to the free parameters involved, we develop a numerical scheme. Of course, many numerical schemes for solving differential equations abound. However, for a scheme to be of any practical value, a necessary condition for its acceptability is its convergence. Our scheme has thus satisfied the necessary and sufficient conditions for convergence; hence, its acceptability. More so, we apply the scheme to solve some practical problems involving differential equations. A comparison of results obtained with exact solutions will further establish the efficiency of this method.