Re. Mickens et I. Ramadhani, FINITE-DIFFERENCE SCHEMES HAVING THE CORRECT LINEAR-STABILITY PROPERTIES FOR ALL FINITE STEP-SIZES-III, Computers & mathematics with applications, 27(4), 1994, pp. 77-84
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.