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A novel meshless method for time Caputo-space Riesz fractional Schrödinger equation

Author

Listed:
  • Habibirad, Ali
  • Baghani, Omid
  • Azin, Hadis
  • Hesameddini, Esmail

Abstract

Usually, in texts about meshless methods, governing equations are determined with integer derivatives in terms of spatial variables. However, in this article, the Schrödinger equation with fractional spatial derivatives of Riesz type is studied. To obtain a numerical solution, the derivatives of shape functions of radial point interpolation are calculated by using the Taylor series expansion for any desired fractional order of the Riesz kind. Additionally, instead of obtaining the general weak form, the weak form is computed over local subdomains. Also, finite difference method is used for discretizing the problem in the time dimension, where the convergence order is O(τ3−β) in this case. Three examples are provided to examine the accuracy of the method. Furthermore, the conservation law of energy will be investigated.

Suggested Citation

  • Habibirad, Ali & Baghani, Omid & Azin, Hadis & Hesameddini, Esmail, 2024. "A novel meshless method for time Caputo-space Riesz fractional Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 446-460.
    • Handle: RePEc:eee:matcom:v:225:y:2024:i:c:p:446-460
    DOI: 10.1016/j.matcom.2024.05.027
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