On The Stability of the Disturbance Algorithm for a Semi-Discrete Scheme of Solution of an Evolutionary Equation in the Banach Space

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Abstract

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.