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Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method. (English) Zbl 1195.81007
Summary: A meshless local boundary integral equation (LBIE) method is proposed to solve the unsteady two-dimensional Schrödinger equation. The method is based on the LBIE with moving least-squares (MLS) approximation. For the MLS approximation, nodal points spread over the analyzed domain are utilized to approximate the interior and boundary variables. A time-stepping method is employed to deal with the time derivative. An efficient method for dealing with singular domain integrations that appear in the discretized equations is presented. Finally, numerical results are considered for some examples to demonstrate the accuracy, efficiency and high rate of convergence of this method.

MSC:
81-08 Computational methods for problems pertaining to quantum theory
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