CONTINUOUS COLLOCATION FORMULATION OF MODIFIED ENRIGHT SECOND DERIVATIVE LINEAR MULTISTEP METHODS FOR STIFF INITIAL VALUE PROBLEMS

Abstract

This paper develops and analyses a family of continuous collocation based second derivative 
linear multistep methods (CC-SDLMMs) for the numerical integration of stiff initial value 
problems (IVPs) in ordinary differential equations (ODEs). Motivated by the modified Enright 
framework in which second derivative information is incorporated at both the initial and terminal 
points of each integration step, we construct a continuous interpolating polynomial through 
collocation at selected grid points, thereby generating a class of methods that are both self-starting 
and yield dense output. We derive the continuous formulation for step numbers