Asymptotic error estimates of a linearized projection-difference method for a differential equation with a monotone operator

In this paper, we study a projection-difference method for the Cauchy problem for an operator-differential equation with a self-adjoint leading operator $A(t)$ and a non-linear monotone subordinate operator $K(\cdot)$ in a Hilbert space. This method leads to solving a system of linear algebraic equations at each time level. Error estimates for the approximate solutions as well as for the fractional powers of the operator $A(t)$ are obtained. The method is applied to a model parabolic problem.