A class of stiffly stable hybrid second derivative continuous linear multistep methods for stiff IVPs in ODEs

No Abstract

Stiffly stable continuous extension of second derivative linear multi-step methods with an off-step point for initial value problems in ordinary differential equations.

In this paper, we introduce a continuous extension of second derivative linear multi-step methods with a hybrid point for the numerical solution of initial valued stiff ordinary differential equations. The continuous extension is based on the Gear's fixed step size backward differential methods [7]. The intervals of absolute stability of methods of step number k&#88047 are determined using the root locus plot. Numerical results of the methods solving a non-linearly stiff initial value problem in ordinary differential equations are compared with that from the state-of-the-art ordinary differential equations code of MATLAB discussed in Higham et al [9]. JONAMP Vol. 11 2007: pp. 175-19

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

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. 159-17