An operational matrix method based on the multivariate Lagrange polynomial for the multi-dimensional nonlinear Schrodinger equation

Zakeri, Ali; Abdolabadi, Fatemeh; Amiraslani, Amirhossein

doi:10.22060/ajmc.2026.24856.1473

An operational matrix method based on the multivariate Lagrange polynomial for the multi-dimensional nonlinear Schrodinger equation

Articles in Press

Document Type : Original Article

Authors

Ali Zakeri ¹

Fatemeh Abdolabadi ¹

Amirhossein Amiraslani ²

¹ Faculty of Mathematics, K. N. Toosi University of Technology, Tehran, Iran

² School of STEM, Department of Mathematics, Capilano University, Canada

10.22060/ajmc.2026.24856.1473

Abstract

In this paper, we give an operational matrix method based on the multivariate Lagrange polynomial basis to find the approximate solution of the multi-dimensional nonlinear Schrodinger (NLS) equation. The NLS equation is discretized through the Leap-Frog method with respect to the time variable. For space discretization, we first compute the differentiation matrix in the multivariate Lagrange polynomial basis. Then the NLS equation is discretized by an operational matrix method. We analyze the unique solvability and stability of the presented method. Finally, in order to observe the validity, effectiveness and accuracy of the proposed method, we give numerical examples for both two and three dimensional NLS equations.

Keywords

Nonlinear Schrodinger equation

Leap-Frog method

Multivariate Lagrange polynomial basis

Matrix of differentiation

Stability

Subjects