Stable multistep methods of numerical integration of rigid systems of differential equations

We consider the basic propositions of the theory of multistep fractional-rational numerical methods with a variable step of integration. We establish general regularities in determining the coefficients of the methods. We prove the A-stability of these methods of arbitrary order, and also the absence of extraneous roots of the characteristic equations of the methods. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 39, No. 2, 1996, pp. 148–152.