In this study three different finite-differences schemes are presented for numerical solution of twodimensional Schrödinger equation. The finite difference schemes developed for this purpose are based on the (1, 5) fully explicit scheme, and the (5, 5) Noye-Hayman fully implicit technique, and the (3, 3) Peaceman and Rachford alternating direction implicit (ADI) formula. These schemes are second order accurate. The results of numerical experiments are presented, and CPU times needed for this problem are reported.
In this paper we have dealt with controlling a boundary condition of a parabolic system in one dimension. This control aims to find the best appropriate right-hand side boundary function which ensures the closeness between the solution of system at final time and the desired target for the solution. Since these types of problems are ill posed, we have used a regularized solution. By numerical examples we have tested the theoretical results.MSC: 35K20; 49J20; 65J20
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