A numerical method for solving the time fractional Schrödinger equation

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Abstract

In this article, we proposed a new numerical method to obtain the approximation solution for the time-fractional Schrödinger equation based on reproducing kernel theory and collocation method. In order to overcome the weak singularity of typical solutions, we apply the integral operator to both sides of differential equation and yield a integral equation. We divided the solution of this kind equation into two parts: imaginary part and real part, and then derived the approximate solutions of the two parts in the form of series with easily computable terms in the reproducing kernel space. New bases of reproducing kernel spaces are constructed and the existence of approximate solution is proved. Numerical examples are given to show the accuracy and effectiveness of our approach.

Keywords

Time-fractional Schrödinger equation Reproducing kernel theory Approximate solutions 

Mathematics Subject Classification (2010)

41A10 41A15 
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Authors and Affiliations

  1. 1.Department of MathematicsHarbin Institute of Technology at WeihaiShandongPeople’s Republic of China

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