Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Fractional ordinary differential equations (34A08)

Cites Work

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A new difference scheme for the time fractional diffusion equation
Optimal error analysis of Crank-Nicolson schemes for a coupled nonlinear Schrödinger system in 3D
Fractional-time Schrödinger equation: fractional dynamics on a comb
A fractional Schrödinger equation and its solution
Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation
Unconditionally optimal error estimates of a linearized Galerkin method for nonlinear time fractional reaction-subdiffusion equations
A numerical method for solving the time fractional Schrödinger equation
Stability and convergence analysis of fully discrete Fourier collocation spectral method for 3-D viscous Burgers' equation
Superconvergence error estimate of a finite element method on nonuniform time meshes for reaction-subdiffusion equations
An efficient energy-preserving method for the two-dimensional fractional Schrödinger equation
A novel scheme to capture the initial dramatic evolutions of nonlinear subdiffusion equations
Unconditionally optimal convergence of a linearized Galerkin FEM for the nonlinear time-fractional mobile/immobile transport equation
Fast L2-1$_\sigma$ Galerkin FEMs for generalized nonlinear coupled Schrödinger equations with Caputo derivatives
A transformed $L 1$ method for solving the multi-term time-fractional diffusion problem
A structure preserving difference scheme with fast algorithms for high dimensional nonlinear space-fractional Schrödinger equations
Subdiffusion with time-dependent coefficients: improved regularity and second-order time stepping
Nonuniform Alikhanov linearized Galerkin finite element methods for nonlinear time-fractional parabolic equations
Sharp $H^1$-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
Semi-implicit Galerkin-Legendre spectral schemes for nonlinear time-space fractional diffusion-reaction equations with smooth and nonsmooth solutions
A fast energy conserving finite element method for the nonlinear fractional Schrödinger equation with wave operator
A weighted ADI scheme for subdiffusion equations
Numerical solution of time fractional Schrödinger equation by using quadratic B-spline finite elements
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
High-order structure-preserving algorithms for the multi-dimensional fractional nonlinear Schrödinger equation based on the SAV approach
Unconditional Convergence and Optimal Error Estimates of a Galerkin-Mixed FEM for Incompressible Miscible Flow in Porous Media
Generalized fractional Schrödinger equation with space-time fractional derivatives
Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
Correction of High-Order BDF Convolution Quadrature for Fractional Evolution Equations
A Discrete Grönwall Inequality with Applications to Numerical Schemes for Subdiffusion Problems
Time fractional Schrödinger equation
A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
Optimal Error Estimates of a Linearized Crank-Nicolson Galerkin FEM for the Kuramoto-Tsuzuki Equations
Finite Difference Schemes for the Variable Coefficients Single and Multi-Term Time-Fractional Diffusion Equations with Non-Smooth Solutions on Graded and Uniform Meshes
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation
Unconditionally Optimal Error Estimates of a Crank--Nicolson Galerkin Method for the Nonlinear Thermistor Equations

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