On the Crank-Nicolson difference scheme for the time-dependent source identification problem

BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2021

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DOI 10.31489/2021m2/35-44
Data confidence 70 medium
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Abstract

In this study the source identification problem for the one-dimensional Schr¨odinger equation with non-local boundary conditions is considered. A second order of accuracy Crank-Nicolson difference scheme for the numerical solution of the differential problem is presented. Stability estimates are proved for the solution of this difference scheme. Numerical results are given.