Unconditional error analysis of the linearized transformed \(L1\) virtual element method for nonlinear coupled time-fractional Schrödinger equations
DOI10.1016/j.cam.2024.116283MaRDI QIDQ6653526
[[Person:6060982|Author name not available (Why is that?)]], Yanping Chen
Publication date: 16 December 2024
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
optimal error estimatesvariables transformationdiscrete complementary convolution kernelsgeneralized nonlinear coupled TFSEslinearized VEM
Fractional derivatives and integrals (26A33) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) 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) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Fractional partial differential equations (35R11) Time-dependent Schrödinger equations and Dirac equations (35Q41)
Cites Work
- Equivalent projectors for virtual element methods
- Virtual element methods for plate bending problems
- Fractional-time Schrödinger equation: fractional dynamics on a comb
- A fractional Schrödinger equation and its solution
- Fractional quantum mechanics and Lévy path integrals
- Virtual element method for two-dimensional linear elasticity problem in mixed weakly symmetric formulation
- A novel scheme to capture the initial dramatic evolutions of nonlinear subdiffusion equations
- 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
- Extended virtual element method for two-dimensional linear elastic fracture
- Conforming and nonconforming conservative virtual element methods for nonlinear Schrödinger equation: a unified framework
- A linearized compact ADI numerical method for the two-dimensional nonlinear delayed Schrödinger equation
- Nonconforming virtual element method for the time fractional reaction-subdiffusion equation with non-smooth data
- The virtual element method for the time fractional convection diffusion reaction equation with non-smooth data
- A local projection stabilization virtual element method for the time-fractional Burgers equation with high Reynolds numbers
- A second-order finite difference scheme for the multi-dimensional nonlinear time-fractional Schrödinger equation
- Optimal error analysis of the alikhanov formula for a time-fractional Schrödinger equation
- Generalized fractional Schrödinger equation with space-time fractional derivatives
- Virtual element methods for parabolic problems on polygonal meshes
- Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
- Time fractional Schrödinger equation
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes
- A Novel Numerical Approach to Time-Fractional Parabolic Equations with Nonsmooth Solutions
- Error analysis of a fully discrete scheme for time fractional Schrödinger equation with initial singularity
- Conforming and nonconforming VEMs for the fourth-order reaction–subdiffusion equation: a unified framework
- The Hitchhiker's Guide to the Virtual Element Method
- A virtual element method with arbitrary regularity
- The virtual element method for solving two-dimensional fractional cable equation on general polygonal meshes
- Linearized transformed \(L1\) Finite element methods for semi-linear time-fractional parabolic problems
- Error estimate of a transformed L1 scheme for a multi-term time-fractional diffusion equation by using discrete comparison principle
- Virtual element method for nonlinear Sobolev equation on polygonal meshes
- Linearized Transformed $L1$ Galerkin FEMs with Unconditional Convergence for Nonlinear Time Fractional Schrödinger Equations
- A transformed \(L1\) Legendre-Galerkin spectral method for time fractional Fokker-Planck equations
- Two-grid finite element method on grade meshes for time-fractional nonlinear Schrödinger equation
- Unconditional error analysis of linearized BDF2 mixed virtual element method for semilinear parabolic problems on polygonal meshes
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