A class of fully discrete approximations for the first order differential equations in banach spaces with uniform estimates on the whole of

Abstract

An initial value problem for a first order differential equation with an operator coefficient in a Banach space is considered. Using the Cayley transform and a projection method we construct a fully discrete approximation which has the spectralproperty with respect to both the time parameter and the spatial parameter. The approximate solution is obtained on the whole with a fixed finite number of “steps”.