Journal
COMPUTATIONAL & APPLIED MATHEMATICS
Volume 39, Issue 2, Pages -Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40314-020-1113-0
Keywords
Schrodinger equation; Radial basis functions; Differential quadrature method; Stability
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Funding
- Council of Scientific and Industrial Research (CSIR), New Delhi, India [25(0299)/19/EMR-II]
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In this article, the authors proposed a meshfree approach for simulation of non-linear Schrodinger equation with constant and variable coefficients. Schrodinger equation is a classical field equation whose principal applications are to the propagation of light in non-linear 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 non-linear 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.
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