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A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity

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Abstract

A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schrödinger (NLS) equations, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.

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Authors and Affiliations

  1. Key Laboratory of Mechanics on Disaster and Environment in Western China, the Ministry of Education, College of Civil Engineering and Mechanics, Lanzhou University, Lanzhou, 730000, China

    Jiaqun Wang, Xiaojing Liu & Youhe Zhou

  2. State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian University of Technology, Dalian, 116024, China

    Xiaojing Liu

Authors
  1. Jiaqun Wang
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  2. Xiaojing Liu
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  3. Youhe Zhou
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Corresponding author

Correspondence to Youhe Zhou.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11502103 and 11421062) and the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China (No.GZ15115)

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Wang, J., Liu, X. & Zhou, Y. A high-order accurate wavelet method for solving Schrödinger equations with general nonlinearity. Appl. Math. Mech.-Engl. Ed. 39, 275–290 (2018). https://doi.org/10.1007/s10483-018-2299-6

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  • DOI: https://doi.org/10.1007/s10483-018-2299-6

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2010 Mathematics Subject Classification

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