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Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations

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  • Pervaiz, Nosheen
  • Aziz, Imran

Abstract

In this study, Haar wavelet collocation method is used for the numerical solution of 1D and 2D cubic nonlinear Schrodinger equations with initial and Dirichlet boundary conditions. The space derivatives are estimated through Haar wavelet collocation method whereas for time derivative we have used Crank–Nicolson scheme. The proposed method is implemented upon several test problems and the numerical results of these test problems establish that the proposed method is accurate.

Suggested Citation

  • Pervaiz, Nosheen & Aziz, Imran, 2020. "Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    • Handle: RePEc:eee:phsmap:v:545:y:2020:i:c:s0378437119320837
    DOI: 10.1016/j.physa.2019.123738
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    References listed on IDEAS

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    1. Ömer Oruç & Alaattin Esen & Fatih Bulut, 2016. "A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-16, September.
    2. Hsiao, Chun-Hui & Wang, Wen-June, 2001. "Haar wavelet approach to nonlinear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(6), pages 347-353.
    3. Hsiao, C.H., 2004. "Haar wavelet approach to linear stiff systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(5), pages 561-567.
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    1. Xuan Liu & Muhammad Ahsan & Masood Ahmad & Muhammad Nisar & Xiaoling Liu & Imtiaz Ahmad & Hijaz Ahmad, 2021. "Applications of Haar Wavelet-Finite Difference Hybrid Method and Its Convergence for Hyperbolic Nonlinear Schr ö dinger Equation with Energy and Mass Conversion," Energies, MDPI, vol. 14(23), pages 1-17, November.

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