Second derivative continuous linear multistep methods for the numerical integration of Stiff system of ordinary differential equations.

Abstract

Continuous linear multi-step methods (CLMM) form a super class of linear multi-step methods (LMM), with properties that embed the characteristics of LMM and hybrid methods. This paper gives a continuous reformulation of the Enright [5] second derivative methods. The motivation lies in the fact that the new formulation offers the advantage of a continuous solution of the initial value problem (IVP) unlike the discrete solution generated from the Enright\'s methods. The success of these methods is in their attainable stiff stability characteristics useful for resolving the problem posed by stiffness in the IVP. In this regard we derive a family of variable order continuous second derivative hybrid methods for the solution of stiff initial value problems in ordinary differential equations. A numerical example is given to demonstrate the application of the methods. JONAMP Vol. 11 2007: pp. 159-174