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Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations

Author

Listed:
  • Yang, Yin
  • Wang, Jindi
  • Zhang, Shangyou
  • Tohidi, Emran

Abstract

In this paper, the space-time Jacobi spectral collocation method (JSC Method) is used to solve the time-fractional nonlinear Schro¨dinger equations subject to the appropriate initial and boundary conditions. At first, the considered problem is transformed into the associated system of nonlinear Volterra integro partial differential equations (PDEs) with weakly singular kernels by the definition and related properties of fractional derivative and integral operators. Therefore, by collocating the associated system of integro-PDEs in both of the space and time variables together with approximating the existing integral in the equation using the Jacobi-Gauss-Type quadrature formula, then the problem is reduced to a set of nonlinear algebraic equations. We can consider solving the system by some robust iterative solvers. In order to support the convergence of the proposed method, we provided some numerical examples and calculated their L∞ norm and weighted L2 norm at the end of the article.

Suggested Citation

  • Yang, Yin & Wang, Jindi & Zhang, Shangyou & Tohidi, Emran, 2020. "Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations," Applied Mathematics and Computation, Elsevier, vol. 387(C).
    • Handle: RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319304680
    DOI: 10.1016/j.amc.2019.06.003
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    Cited by:

    1. Li, Lili & Zhao, Dan & She, Mianfu & Chen, Xiaoli, 2022. "On high order numerical schemes for fractional differential equations by block-by-block approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Sun, Lin & Chen, Yiming & Dang, Rongqi & Cheng, Gang & Xie, Jiaquan, 2022. "Shifted Legendre polynomials algorithm used for the numerical analysis of viscoelastic plate with a fractional order model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 193(C), pages 190-203.

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