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A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation. (English) Zbl 1463.65323

Summary: In this article, the authors propose a meshfree approach for simulation of nonlinear Schrödinger equation with constant and variable coefficients. Schrödinger equation is a classical field equation whose principal applications are to the propagation of light in nonlinear optical fibers and planar waveguides and in quantum mechanics. First of all, spatial derivatives are discretized by using local radial basis functions based on differential quadrature method (LRBF-DQM) and, subsequently, the obtained system of nonlinear ordinary differential equations (ODEs) is solved by fourth-order Runge-Kutta (RK-4). The stability analysis of the proposed approach is discussed by the matrix method. Numerical experiments ensure that the proposed approach is accurate and computationally efficient.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35Q55 NLS equations (nonlinear Schrödinger equations)
65D12 Numerical radial basis function approximation
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
78A60 Lasers, masers, optical bistability, nonlinear optics
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65D30 Numerical integration

Software:

Matlab
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Full Text: DOI

References:

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