The sinc-collocation and sinc-Galerkin methods for solving the two-dimensional Schrödinger equation with nonhomogeneous boundary conditions

DOI10.1016/j.apm.2013.04.043zbMath1427.65284OpenAlexW2066407037MaRDI QIDQ1792040

Mehdi Dehghan, Faezeh Emami-Naeini

Publication date: 11 October 2018

Published in: Applied Mathematical Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apm.2013.04.043

zbMATH Keywords

Schrödinger equationnonhomogeneous boundary conditionssinc-Galerkin methodsinc-collocation methodsinc numerical methods

Mathematics Subject Classification ID

Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70)

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Uses Software

• Sinc-Pack

Cites Work

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• The use of sinc-collocation method for solving multi-point boundary value problems
• The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
• The sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients
• Double exponential transformation in the sinc-collocation method for a boundary value problem with fourth-order ordinary differential equation
• A compact split-step finite difference method for solving the nonlinear Schrödinger equations with constant and variable coefficients
• High-order compact ADI (HOC-ADI) method for solving unsteady 2D Schrödinger equation
• Fourth-order alternating direction implicit compact finite difference schemes for two-dimensional Schrödinger equations
• The use of compact boundary value method for the solution of two-dimensional Schrödinger equation
• An alternating-direction sinc-Galerkin method for elliptic problems
• Wave propagation and underwater acoustics
• Operations on oscillatory functions
• Recent developments of the Sinc numerical methods.
• Sinc-Galerkin method based on the DE transformation for the boundary value problem of fourth-order ODE
• Application of the sinc method to a dynamic elasto-plastic problem
• A semi-discrete higher order compact scheme for the unsteady two-dimensional Schrödinger equation
• A numerical method for two-dimensional Schrödinger equation using collocation and radial basis functions
• Finite difference procedures for solving a problem arising in modeling and design of certain optoelectronic devices
• The use of Sinc-collocation method for solving Falkner-Skan boundary-layer equation
• Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method
• Symmetrization of the Sinc-Galerkin Method with Block Techniques for Elliptic Equations
• The Sinc-Galerkin Method for Fourth-Order Differential Equations
• On the finite-differences schemes for the numerical solution of two dimensional Schrödinger equation
• Numerical schemes for the simulation of the two-dimensional Schrödinger equation using non-reflecting boundary conditions
• The numerical solution of third‐order boundary value problems using Sinc‐collocation method
• Algorithm 432 [C2: Solution of the matrix equation AX + XB = C [F4]]

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