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

Yin Yang, Jindi Wang, Shangyou Zhang and Emran Tohidi

Applied Mathematics and Computation, 2020, vol. 387, issue C

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.

Keywords: Convergence analysis; Time-fractional Schro¨dinger equation; Jacobi spectral-collocation method; Gauss-type quadrature (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:387:y:2020:i:c:s0096300319304680

DOI: 10.1016/j.amc.2019.06.003

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