PRINCIPLE OF MULTIPLICATION AND IDENTIFICATION OF THE MAIN PART OF THE MAPPING WHEN SOLVING NUMERICALLY THE STIFF SYSTEM OF NON-LINEAR DIFFERENTIAL EQUATIONS

N.Yu. Bakaev, V.N. Mikhailov
VANT. Ser.: Mat. Mod. Fiz. Rroc 1990. Вып.3. С. 10-14.

      A new approach to efficient numerical solution of stiff systems of non-linear differential equations is suggested. A principle of multiplication and identification of the main part of the mapping that predetermines this stiff system formulated in this work lies in the basis of this approach.

      A stability theory of additive difference schemes in Banach spaces is described. The produced estimations of stability are the generalization of the results produced by the author on the stability of non-split difference schemes. And the components of the initial operator splitting are not supposed to be commutating, but we need them to be close to the commutating in the sense specified in the paper. The results of the work can be applied to the additive schemes both with constant and with alternating transition operator. Stability estimations for additive schemes with perturbed operators are constructed.