Numerical Approximation of One- and Two-Dimensional Coupled Nonlinear Schrödinger Equation by Implementing Barycentric Lagrange Interpolation Polynomial DQM | Zendy

Varun Joshi | Zendy; Mamta Kapoor | Zendy; Nitin Bhardwaj | Zendy; Mehedi Masud | Zendy; Jehad F. AlAmri | Zendy

Open Access

Numerical Approximation of One- and Two-Dimensional Coupled Nonlinear Schrödinger Equation by Implementing Barycentric Lagrange Interpolation Polynomial DQM

Author(s) -

Varun Joshi,

Mamta Kapoor,

Nitin Bhardwaj,

Mehedi Masud,

Jehad F. AlAmri

Publication year - 2021

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2021/9968063

Subject(s) - barycentric coordinate system , lagrange polynomial , mathematics , discretization , interpolation (computer graphics) , polynomial interpolation , nonlinear system , mathematical analysis , numerical analysis , quadrature (astronomy) , polynomial , ordinary differential equation , numerical stability , partial differential equation , differential equation , linear interpolation , geometry , computer science , motion (physics) , physics , quantum mechanics , artificial intelligence , electrical engineering , engineering

In this paper, a new numerical method named Barycentric Lagrange interpolation-based differential quadrature method is implemented to get numerical solution of 1D and 2D coupled nonlinear Schrödinger equations. In the present study, spatial discretization is done with the aid of Barycentric Lagrange interpolation basis function. After that, a reduced system of ordinary differential equations is solved using strong stability, preserving the Runge-Kutta 43 method. In order to check the accuracy of the proposed scheme, we have used the formula of L ∞ error norm. The matrix stability analysis method is implemented to test the proposed method’s stability, which confirms that the proposed scheme is unconditionally stable. The present scheme produces better results, and it is easy to implement to obtain numerical solutions of a class of partial differential equations.

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