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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.

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Authors and Affiliations

  1. Department of Mathematics, Harbin Institute of Technology at Weihai, Shandong, 264209, People’s Republic of China

    Na Liu & Wei Jiang

Authors
  1. Na Liu
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  2. Wei Jiang
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Corresponding author

Correspondence to Wei Jiang.

Additional information

Communicated by: Martin Stynes

The authors would like to express their thanks to the unknown referees for their careful reading, helpful comments and valuable suggestions. The work was supported by the National Natural Science Foundation of China (Grant No. 11401139) and State Scholarship Fund (File No.201706125045).

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Liu, N., Jiang, W. A numerical method for solving the time fractional Schrödinger equation. Adv Comput Math 44, 1235–1248 (2018). https://doi.org/10.1007/s10444-017-9579-z

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  • DOI: https://doi.org/10.1007/s10444-017-9579-z

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