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A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation

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Abstract

In this article, the authors proposed a meshfree approach for simulation of non-linear Schrödinger equation with constant and variable coefficients. Schrödinger 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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Acknowledgements

The work was supported by the Council of Scientific and Industrial Research (CSIR), New Delhi, India, with grant No.25(0299)/19/EMR-II.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    Ram Jiwari, Sanjay Kumar, R. C. Mittal & Jan Awrejcewicz

  2. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland

    Ram Jiwari, Sanjay Kumar, R. C. Mittal & Jan Awrejcewicz

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  1. Ram Jiwari
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  2. Sanjay Kumar
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Correspondence to Ram Jiwari.

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Communicated by Antonio José Silva Neto.

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Jiwari, R., Kumar, S., Mittal, R.C. et al. A meshfree approach for analysis and computational modeling of non-linear Schrödinger equation. Comp. Appl. Math. 39, 95 (2020). https://doi.org/10.1007/s40314-020-1113-0

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