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Numerical Simulation of a Non-linear Singular Perturbed Schrödinger Equation Using Finite Element Approximation

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Abstract

This paper is concerned with the various finite element solutions of non-linear singularly perturbed Schrödinger boundary value problems. Non-linear Schrödinger equation does not appear to have been previously studied in detail computationally and it is hope that this paper will help to provide a new idea in this direction. To linearize the nonlinear system of equations, we introduced a concept of new modified fifth order Newton type iterative method and discussed the behavior of the solution. In order to confirm our theoretical results, numerically and to demonstrate the performance of the proposed algorithm, we have considered two examples of non-linear Schrödinger’s equation involving non-linearity in homogenous and non-homogenous form.

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Acknowledgments

The first and third author wish to express his appreciation for the financial support provided by Department of Science and Technology, New Delhi India under research grant sanction order No. SR/FTP/MS-14/2007. The authors also extend their appreciation to anonymous reviewers for their valuable suggestions to improve the quality of this paper.

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Authors and Affiliations

  1. Department of Mathematics, Motilal Nehru National Institute of Technology, Allahabad, 211004, UP, India

    Manoj Kumar, Akanksha Srivastava & Garima Mishra

Authors
  1. Manoj Kumar
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  2. Akanksha Srivastava
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  3. Garima Mishra
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Corresponding author

Correspondence to Akanksha Srivastava.

Appendix

Appendix

Matlab Code for the Solution of Singularly Perturbed Non-Linear Schrödinger equation

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Kumar, M., Srivastava, A. & Mishra, G. Numerical Simulation of a Non-linear Singular Perturbed Schrödinger Equation Using Finite Element Approximation. Natl. Acad. Sci. Lett. 36, 239–252 (2013). https://doi.org/10.1007/s40009-013-0125-3

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