An Alternative Implementation of Variable Step-Size Multistep Formulas for Stiff ODEs

Abstract

An alternative technique for the implementation of variable step-size multistep formulas is developed for the numerical solution of ordinary differential equations. Formulas based on this technique have the property that their leading coefficients are constant; thLs LS important for methods which solve stiff systems. In addition, both theoretmal and empirical results indicate that methods based on this techmque have stability properties similar to those of the corresponding variable coefficient implementations. As a particular example, we have nnplemented the backward differentiation formulas m this form, and the numerical results look very promising.