The new class of A-stable hybrid multistep methods for numerical solution of stiff initial value problem

Abstract

In this paper, we present a class of   hybrid multistep methods for the numerical solution

of first-order initial value problems. We have used second derivative of solution (similar to second derivative multistep methods of Enright) and  an off-step point. The accuracy and stability analysis are discussed. Stability domains of our presented methods have been obtained?, ?showing that this class of efficient numerical methods are A))-stable of order up to 10. Numerical results are also given for four test problems?.

Keywords: Initial value problems, Multistep methods, Off-step point, Stability aspects.