Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes

DOI10.1080/00207160.2022.2070842OpenAlexW4224921478MaRDI QIDQ5044150

Shujuan Lü, Li Chen

Publication date: 24 October 2022

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2022.2070842

zbMATH Keywords

convergencefinite difference methodspectral methodtime fractional Schrödinger equationweak singularity

Mathematics Subject Classification ID

Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (2)

A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation ⋮ Space-time methods based on isogeometric analysis for time-fractional Schrödinger equation

Cites Work

• Unnamed Item
• Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems
• Fractional-time Schrödinger equation: fractional dynamics on a comb
• A second-order accurate numerical method for a fractional wave equation
• Interpolation approximations based on Gauss-Lobatto-Legendre-Birkhoff quadrature
• The nonlinear Schrödinger equation in the finite line
• Fractional quantum mechanics and Lévy path integrals
• Linearized compact ADI schemes for nonlinear time-fractional Schrödinger equations
• A second-order implicit difference scheme for the nonlinear time-space fractional Schrödinger equation
• Error analysis of a second-order method on fitted meshes for a time-fractional diffusion problem
• Fourier spectral approximation for time fractional Burgers equation with nonsmooth solutions
• Two second-order and linear numerical schemes for the multi-dimensional nonlinear time-fractional Schrödinger equation
• Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation
• Global consistency analysis of L1-Galerkin spectral schemes for coupled nonlinear space-time fractional Schrödinger equations
• An L1 Legendre-Galerkin spectral method with fast algorithm for the two-dimensional nonlinear coupled time fractional Schrödinger equation and its parameter estimation
• Time fractional Schrödinger equation revisited
• Boundary layers and emitted excitations in nonlinear Schrödinger superflow past a disk
• Convergence analysis of space-time Jacobi spectral collocation method for solving time-fractional Schrödinger equations
• 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
• A Second-Order Scheme with Nonuniform Time Steps for a Linear Reaction-Subdiffusion Problem
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
• Error analysis of the L1 method on graded and uniform meshes for a fractional-derivative problem in two and three dimensions
• Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

This page was built for publication: Spectral approximation for nonlinear time fractional Schrödinger equation on graded meshes