Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain

NLS equations (nonlinear Schrödinger equations) (35Q55) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Fractional partial differential equations (35R11)

Related Items (1)

A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley-Torvik differential equation

Cites Work

Unnamed Item
Spectral and pseudospectral approximations for the time fractional diffusion equation on an unbounded domain
An improved collocation method for multi-dimensional space-time variable-order fractional Schrödinger equations
Fourth-order compact and energy conservative difference schemes for the nonlinear Schrödinger equation in two dimensions
Jacobi-Gauss-Lobatto collocation method for the numerical solution of $1+1$ nonlinear Schrödinger equations
A fully spectral collocation approximation for multi-dimensional fractional Schrödinger equations
Compact finite difference schemes with high accuracy for one-dimensional nonlinear Schrödinger equation
Highly accurate numerical schemes for multi-dimensional space variable-order fractional Schrödinger equations
The stability and convergence of an explicit difference scheme for the Schrödinger equation on an infinite domain by using artificial boundary conditions
An alternating direction implicit spectral method for solving two dimensional multi-term time fractional mixed diffusion and diffusion-wave equations
Solution of multi-dimensional Klein-Gordon-Zakharov and Schrödinger/Gross-Pitaevskii equations via local radial basis functions-differential quadrature (RBF-DQ) technique on non-rectangular computational domains
A reliable numerical algorithm for the fractional vibration equation
A numerical scheme based on radial basis function finite difference (RBF-FD) technique for solving the high-dimensional nonlinear Schrödinger equations using an explicit time discretization: Runge-Kutta method
Numerical simulation of multi-dimensional distributed-order generalized Schrödinger equations
Local discontinuous Galerkin methods for nonlinear Schrödinger equations
Multi-dimensional spectral tau methods for distributed-order fractional diffusion equations
DMLPG method for numerical simulation of soliton collisions in multi-dimensional coupled damped nonlinear Schrödinger system which arises from Bose-Einstein condensates
The Laguerre-Hermite spectral methods for the time-fractional sub-diffusion equations on unbounded domains
Singularity preserving spectral collocation method for nonlinear systems of fractional differential equations with the right-sided Caputo fractional derivative
Spectral method for the two-dimensional time distributed-order diffusion-wave equation on a semi-infinite domain
An efficient hybrid numerical scheme for nonlinear multiterm Caputo time and Riesz space fractional-order diffusion equations with delay
An energy-preserving computational approach for the semilinear space fractional damped Klein-Gordon equation with a generalized scalar potential
Computational method for reaction diffusion-model arising in a spherical catalyst
Computational and theoretical aspects of Romanovski-Bessel polynomials and their applications in spectral approximations
An alternating direction implicit Legendre spectral method for simulating a 2D multi-term time-fractional Oldroyd-B fluid type diffusion equation
Several conservative compact schemes for a class of nonlinear Schrödinger equations with wave operator
Jacobi collocation method for the approximate solution of some fractional-order Riccati differential equations with variable coefficients
An accurate spectral collocation method for nonlinear systems of fractional differential equations and related integral equations with nonsmooth solutions
A priori error estimates of a Jacobi spectral method for nonlinear systems of fractional boundary value problems and related Volterra-Fredholm integral equations with 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
An efficient dissipation-preserving Legendre-Galerkin spectral method for the Higgs boson equation in the de Sitter spacetime universe
A unified spectral collocation method for nonlinear systems of multi-dimensional integral equations with convergence analysis
Finite difference Laguerre-Legendre spectral method for the two-dimensional generalized Oldroyd-B fluid on a semi-infinite domain
Computational aspects of fractional Romanovski-Bessel functions
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
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
A novel spectral Galerkin/Petrov-Galerkin algorithm for the multi-dimensional space-time fractional advection-diffusion-reaction equations with nonsmooth solutions
An easy to implement linearized numerical scheme for fractional reaction-diffusion equations with a prehistorical nonlinear source function
Sharp Error Bounds for Jacobi Expansions and Gegenbauer--Gauss Quadrature of Analytic Functions
Spectral Methods
Optimal H¹ Estimates for two Time-discrete Galerkin Approximations of a Nonlinear Schrödinger Equation
Unconditionally Convergent $L1$-Galerkin FEMs for Nonlinear Time-Fractional Schrödinger Equations
Convergence analysis of an L1-continuous Galerkin method for nonlinear time-space fractional Schrödinger equations
Legendre spectral method for the fractional Bratu problem
Optimal systems of nodes for Lagrange interpolation on bounded intervals. A survey
On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra–Fredholm integral equations
Chebyshev spectral methods for multi-order fractional neutral pantograph equations
Combined Galerkin spectral/finite difference method over graded meshes for the generalized nonlinear fractional Schrödinger equation

This page was built for publication: Tanh Jacobi spectral collocation method for the numerical simulation of nonlinear Schrödinger equations on unbounded domain