Numerical study of generalized 2-D nonlinear Schrödinger equation using Kansa method

DOI10.1016/j.matcom.2022.04.030OpenAlexW4225391633WikidataQ113869143 ScholiaQ113869143MaRDI QIDQ2672393

Maheshwar Pathak, Pratibha Joshi, Kottakkaran Sooppy Nisar

Publication date: 8 June 2022

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

Full work available at URL: https://doi.org/10.1016/j.matcom.2022.04.030

zbMATH Keywords

Schrödinger equationpartial differential equationnonlinear equationradial basis functionKansa method

Mathematics Subject Classification ID

Numerical analysis (65-XX) Optics, electromagnetic theory (78-XX)

Uses Software

• Matlab

Cites Work

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• Time-splitting pseudo-spectral domain decomposition method for the soliton solutions of the one- and multi-dimensional nonlinear Schrödinger equations
• Space-fractional advection-dispersion equations by the Kansa method
• The meshless local Petrov-Galerkin (MLPG) method for the generalized two-dimensional nonlinear Schrödinger equation
• Governing equations of envelopes created by nearly bichromatic waves on deep water
• Meshfree explicit local radial basis function collocation method for diffusion problems
• Fractional diffusion equations by the Kansa method
• A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics
• A finite-difference method for the numerical solution of the Schrödinger equation
• The use of proper orthogonal decomposition (POD) meshless RBF-FD technique to simulate the shallow water equations
• Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
• Support-vector networks
• Two numerical meshless techniques based on radial basis functions (RBFs) and the method of generalized moving least squares (GMLS) for simulation of coupled Klein-Gordon-Schrödinger (KGS) equations
• Numerical soliton solutions of fractional Newell-Whitehead-Segel equation in binary fluid mixtures
• A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation
• An adaptive LOOCV-based refinement scheme for RBF collocation methods over irregular domains
• A two-stage adaptive scheme based on RBF collocation for solving elliptic PDEs
• Development of the Kansa method for solving seepage problems using a new algorithm for the shape parameter optimization
• A new semi-analytical method for solving a class of time fractional partial differential equations with variable coefficients
• The meshless Kansa method for time-fractional higher order partial differential equations with constant and variable coefficients
• Numerical solution of nonlinear Schrödinger equation with Neumann boundary conditions using quintic B-spline Galerkin method
• The improved complex variable element-free Galerkin method for two-dimensional Schrödinger equation
• A meshfree method for the solution of two-dimensional cubic nonlinear 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
• A new method for the numerical solution of the Schrödinger equations
• THE METHOD OF APPROXIMATE PARTICULAR SOLUTIONS FOR SOLVING ELLIPTIC PROBLEMS WITH VARIABLE COEFFICIENTS
• Meshless Local Petrov-Galerkin (MLPG) Mixed Collocation Method For Elasticity Problems
• Analysis of Transient Heat Conduction in 3D Anisotropic Functionally Graded Solids, by the MLPG Method
• Numerical solution to the unsteady two-dimensional Schrödinger equation using meshless local boundary integral equation method
• Iterative Solution of Systems Originating from Integral Equations and Surface Interpolation
• A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation
• Scattered Data Interpolation: Tests of Some Method
• Radial Basis Functions
• On the finite-differences schemes for the numerical solution of two dimensional Schrödinger equation
• Kansa RBF method for nonlinear problems