On the stability of the disturbance algorithm for a semi-discrete scheme of solution of an evolutionary equation in the Banach space

A purely implicit three-layer semi-discrete scheme of second-order approximation is considered in the Banach space. The three-layer semi-discrete scheme is reduced by means of the disturbance algorithm to two two-layer schemes. Using the solutions of these schemes, we construct an approximate solution of the initial problem. The stability of the constructed scheme is proved.