Non-polynomial spline method for the time-fractional nonlinear Schrödinger equation
From MaRDI portal
Publication:1715568
DOI10.1186/s13662-018-1743-3zbMath1448.65187OpenAlexW2891932337MaRDI QIDQ1715568
Qiang Xu, Mingzhu Li, Xiao-Hua Ding
Publication date: 28 January 2019
Published in: Advances in Difference Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1186/s13662-018-1743-3
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) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)
Related Items
Quintic non-polynomial spline for time-fractional nonlinear Schrödinger equation, A fourth order non-polynomial quintic spline collocation technique for solving time fractional superdiffusion equations, Non-polynomial B-spline and shifted Jacobi spectral collocation techniques to solve time-fractional nonlinear coupled Burgers' equations numerically, Numerical treatments of the nonlinear coupled time‐fractional Schrödinger equations, A new high-accuracy difference method for nonhomogeneous time-fractional Schrödinger equation, Application of the B-Spline Galerkin approach for approximating the time-fractional Burger's equation, Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation
Cites Work
- Unnamed Item
- Tension spline method for solution of non-linear Fisher equation
- Solving the time-fractional Schrödinger equation by Krylov projection methods
- A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
- Mixed spline function method for reaction-subdiffusion equations
- Non-polynomial quintic spline solution for the system of third order boundary-value problems
- Numerical studies of the cubic non-linear Schrödinger equation
- Non-polynomial spline method for the solution of two-dimensional linear wave equations with a nonlinear source term
- A stable numerical method for multidimensional time fractional Schrödinger equations
- Fractional-time Schrödinger equation: fractional dynamics on a comb
- Quintic nonpolynomial spline method for the solution of a second-order boundary-value problem with engineering applications
- Parametric spline functions for the solution of the one time fractional Burgers equation
- Finite difference approximations for the fractional Fokker-Planck equation
- Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
- Polynomial and nonpolynomial spline methods for fractional sub-diffusion equations
- A higher order non-polynomial spline method for fractional sub-diffusion problems
- A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations
- Waiting-times and returns in high-frequency financial data: An empirical study
- Fractional Schrödinger equations with potential and optimal controls
- Numerical solution of the regularized long wave equation using nonpolynomial splines
- A fully discrete difference scheme for a diffusion-wave system
- Quadratic non-polynomial spline approach to the solution of a system of second-order boundary-value problems
- 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
- Quintic spline technique for time fractional fourth-order partial differential equation
- Applications of Fractional Calculus to the Theory of Viscoelasticity
- Time fractional Schrödinger equation
- Septic spline function method for nonlinear Schrödinger equations
- Operational method for solving fractional differential equations using cubic B-spline approximation
- Numerical solution of time-fractional fourth-order partial differential equations
- Error and stability analysis of numerical solution for the time fractional nonlinear Schrödinger equation on scattered data of general‐shaped domains
- B‐spline solution of fractional integro partial differential equation with a weakly singular kernel
- Non-polynomial spline for solution of boundary-value problems in plate deflection theory