FINITE-DIFFERENCE SCHEMES HAVING THE CORRECT LINEAR-STABILITY PROPERTIES FOR ALL FINITE STEP-SIZES-III

We construct a class of finite-difference schemes for two coupled firs t-order ordinary differential equations such that the difference equat ions have the correct linear stability properties for all finite value s of the step-size. The differential equations considered are assumed to have only a single (real) fixed-point. A major consequence of such schemes is the absence of elementary numerical instabilities. Illustra tions of such schemes are given for the Duffing and van der Pol equati ons.