Numerical Solution of Linear and Nonlinear Schrödinger Equation via Shifted Chebyshev Collocation Method

Articles in Press

Document Type : Research Paper

Authors

Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University), Haridwar, Uttarakhand.

Abstract

The present study focuses on numerical solutions of linear and nonlinear Schrödinger equation subject to initial and boundary conditions employing shifted Chebyshev spectral collocation method (SCSCM). In the solution procedure, unknown function and its space derivatives have been approximated employing shifted Chebyshev polynomials and their derivatives, respectively, together with Chebyshev-Gauss-Lobatto points. The present collocation method transforms Schrödinger equation into a system of ordinary differential equations (ODEs). Thereafter, obtained system has been solved employing fourth order Runge-Kutta scheme. In order to demonstrate accuracy and efficiency of the present method, a comparison of present numerical solutions of different examples of Schrödinger equation with exact and approximate solutions available in literature has been discussed. The SCSCM can be implemented to solve second and higher order linear and nonlinear partial differential equations (PDEs) arising in physics, mechanics and biophysics.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 21 December 2024

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History

  • Receive Date: 10 July 2023
  • Revise Date: 14 November 2024
  • Accept Date: 09 December 2024

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