One-Step A-Stable Implicit Block Method for Approximating the Solutions of First Order Stiff Ordinary Differential Equations

Abstract ―​

A self-starting A-stable implicit linear multistep block method for approximating stiff initial value problems (IVPs) in ordinary differential equations (ODEs) is developed. The construction was carried out by pairing a three-step top order method (TOM) and a four-step linear multistep method and shifting each equation four times to form a block method that generates approximations on ten grid points simultaneously. The implementation of the method on some stiff ODEs confirms its efficiency.