A Family of Continuous Blended Block A-Stable Second Derivative Linear Multistep Methods for the solutions of Stiff System of Ordinary Differential Equations

Abstract

In this paper, the formulation of the block second derivative Blended Linear Multistep methods for step numbers k=5,6 and7 was considered. We present a new family of blended block A-stable second derivative linear multistep methods of order p=k+2 for step numbers k=5,6 and 7 for the solution of stiff initial value problems. The newly constructed blended block methods are all A-stable, consistent, zero-stable and as such convergent. Numerical examples are considered to show the performance of the new methods.