Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation

DOI10.1016/j.matcom.2020.02.017zbMath1453.65325OpenAlexW3008945563MaRDI QIDQ2221542

Yanyan Li

Publication date: 2 February 2021

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2020.02.017

zbMATH Keywords

Galerkin finite element methodB-splinecoupled Schrödinger equation

Mathematics Subject Classification ID

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)

Related Items (7)

A Galerkin approach to solitary wave propagation for the second-order nonlinear evolution equation based on quartic B-spline functions ⋮ Time-splitting Galerkin method for spin-orbit-coupled Bose-Einstein condensates ⋮ Error estimates of second-order BDF Galerkin finite element methods for a coupled nonlinear Schrödinger system ⋮ Galerkin approximation with quintic B-spline as basis and weight functions for solving second order coupled nonlinear Schrödinger equations ⋮ Unconditional optimal error estimates of a linearized mass- and energy-conservation FEM for a coupled nonlinear Schrödinger equations ⋮ A unified framework of high order structure-preserving B-splines Galerkin methods for coupled nonlinear Schrödinger systems ⋮ A strong-form local meshless approach based on radial basis function-finite difference (RBF-FD) method for solving multi-dimensional coupled damped Schrödinger system appearing in Bose-Einstein condensates

Cites Work

• Crank-Nicolson difference scheme for the coupled nonlinear Schrödinger equations with the Riesz space fractional derivative
• A collocation solution for Burgers' equation using cubic B-spline finite elements
• Numerical method using cubic trigonometric B-spline technique for nonclassical diffusion problems
• Finite element method with discrete transparent boundary conditions for the time-dependent 1D Schrödinger equation
• A Chebyshev pseudospectral multidomain method for the soliton solution of coupled nonlinear Schrödinger equations
• A quadratic B-spline finite element method for solving nonlinear Schrödinger equation
• Numerical solution of nonlinear Schrödinger equation with Neumann boundary conditions using quintic B-spline Galerkin method
• Numerical solution of the Schrödinger equations by using Delta-shaped basis functions
• A numerical solution of the RLW equation by Galerkin method using quartic B‐splines
• Taylor‐Galerkin B‐spline finite element method for the one‐dimensional advection‐diffusion equation

This page was built for publication: Cubic B-spline Galerkin method for numerical solution of the coupled nonlinear Schrödinger equation