Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
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Publication:5031277
DOI10.1080/00207160.2020.1822994zbMath1480.65275OpenAlexW3084856537MaRDI QIDQ5031277
Ahmed S. Hendy, Mahmoud A. Zaky
Publication date: 18 February 2022
Published in: International Journal of Computer Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1080/00207160.2020.1822994
theoretical analysistime-space fractional Schrödinger equationdiscrete Grönwall inequality\(L1\)-type schemespectral approximation of Galerkin form
Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional partial differential equations (35R11)
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Cites Work
- Unnamed Item
- An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
- A new difference scheme for the time fractional diffusion equation
- A second order finite difference-spectral method for space fractional diffusion equations
- Galerkin finite element method for nonlinear fractional Schrödinger equations
- A fourth-order implicit-explicit scheme for the space fractional nonlinear Schrödinger equations
- A priori estimates for solutions of boundary value problems for fractional-order equations
- Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
- Generalized finite difference/spectral Galerkin approximations for the time-fractional telegraph equation
- The locally extrapolated exponential splitting scheme for multi-dimensional nonlinear space-fractional Schrödinger equations
- Dissipativity of semilinear time fractional subdiffusion equations and numerical approximations
- Numerical simulation of multi-dimensional distributed-order generalized Schrödinger equations
- A Legendre spectral method on graded meshes for the two-dimensional multi-term time-fractional diffusion equation with non-smooth solutions
- Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations
- Exponential Jacobi-Galerkin method and its applications to multidimensional problems in unbounded domains
- A Crank-Nicolson ADI Galerkin-Legendre spectral method for the two-dimensional Riesz space distributed-order advection-diffusion equation
- A novel discrete Gronwall inequality in the analysis of difference schemes for time-fractional multi-delayed diffusion equations
- Existence, uniqueness and numerical analysis of solutions of tempered fractional boundary value problems
- A compact fourth-order in space energy-preserving method for Riesz space-fractional nonlinear wave equations
- An unstructured mesh control volume method for two-dimensional space fractional diffusion equations with variable coefficients on convex domains
- Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions
- Crank-Nicolson/Galerkin spectral method for solving two-dimensional time-space distributed-order weakly singular integro-partial differential equation
- Convergence and stability of compact finite difference method for nonlinear time fractional reaction-diffusion equations with delay
- Finite difference/spectral approximations for the time-fractional diffusion equation
- Galerkin-Legendre spectral schemes for nonlinear space fractional Schrödinger equation
- Error estimates of spectral Galerkin methods for a linear fractional reaction-diffusion equation
- On the solution of hyperbolic two-dimensional fractional systems via discrete variational schemes of high order of accuracy
- A novel alternating-direction implicit spectral Galerkin method for a multi-term time-space fractional diffusion equation in three dimensions
- Spectral Methods
- Variational solution of fractional advection dispersion equations on bounded domains in ℝd
- Generalized fractional Schrödinger equation with space-time fractional derivatives
- Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
- Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
- A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
- Time fractional Schrödinger equation
- Fractional pseudo-spectral methods for distributed-order fractional PDEs
- Analysis of L1-Galerkin FEMs for Time-Fractional Nonlinear Parabolic Problems
- Efficient Numerical Computation of Time-Fractional Nonlinear Schrödinger Equations in Unbounded Domain
- A Crank--Nicolson ADI Spectral Method for a Two-Dimensional Riesz Space Fractional Nonlinear Reaction-Diffusion Equation
- Finite difference method for time-space-fractional Schrödinger equation
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
