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A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation

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  • Ahsan, Muhammad
  • Ahmad, Imtiaz
  • Ahmad, Masood
  • Hussian, Iltaf

Abstract

In this research work, we proposed a Haar wavelet collocation method (HWCM) for numerical solution of linear and nonlinear Schrödinger equations. The nonlinear term present in the model equation is linearized by a linearization technique. The Time derivative in the Schrödinger equation is approximated by forward Euler difference formula while the space derivatives are approximated by Haar function, which convert the model equation into system of algebraic equation. The stability analysis of the HWCM is also given. Several test problems are presented to verify the accuracy, stability and capability of the proposed method.

Suggested Citation

  • Ahsan, Muhammad & Ahmad, Imtiaz & Ahmad, Masood & Hussian, Iltaf, 2019. "A numerical Haar wavelet-finite difference hybrid method for linear and non-linear Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 13-25.
    • Handle: RePEc:eee:matcom:v:165:y:2019:i:c:p:13-25
    DOI: 10.1016/j.matcom.2019.02.011
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Ahsan, Muhammad & Bohner, Martin & Ullah, Aizaz & Khan, Amir Ali & Ahmad, Sheraz, 2023. "A Haar wavelet multi-resolution collocation method for singularly perturbed differential equations with integral boundary conditions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 166-180.
    2. 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.
    3. Ahsan, Muhammad & Lei, Weidong & Bohner, Martin & Khan, Amir Ali, 2024. "A high-order multi-resolution wavelet method for nonlinear systems of differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 543-559.

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