A numerical method for solving the time fractional Schrödinger equation
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Publication:1670414
DOI10.1007/S10444-017-9579-ZzbMath1398.65319OpenAlexW2780091894MaRDI QIDQ1670414
Publication date: 5 September 2018
Published in: Advances in Computational Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10444-017-9579-z
Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Fractional partial differential equations (35R11)
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Cites Work
- Error estimates for approximations of distributed order time fractional diffusion with nonsmooth data
- Solving the time-fractional Schrödinger equation by Krylov projection methods
- Blowup dynamics for smooth data equivariant solutions to the critical Schrödinger map problem
- A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
- Approximate solution of the fractional advection-dispersion equation
- The Galerkin finite element method for a multi-term time-fractional diffusion equation
- Simplified reproducing kernel method for fractional differential equations with delay
- Monotonicity properties of the blow-up time for nonlinear Schrödinger equations: numerical evidence
- Fractional differential equations and the Schrödinger equation
- Small data blow-up for a system of nonlinear Schrödinger equations
- Solving a system of linear Volterra integral equations using the new reproducing kernel method
- The use of a meshless technique based on collocation and radial basis functions for solving the time fractional nonlinear Schrödinger equation arising in quantum mechanics
- On the blowing up of solutions to the Cauchy problem for nonlinear Schrödinger equations
- Theory of Reproducing Kernels
- The random walk's guide to anomalous diffusion: A fractional dynamics approach
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