Open AccessA Wavelet-Galerkin Method for the Nonlinear Schrödinger Equation
Author(s) -
Yacine Benhadid
Publication year - 2021
Publication title -
asian research journal of mathematics
Language(s) - English
Resource type - Journals
ISSN - 2456-477X
DOI - 10.9734/arjom/2021/v17i1130343
Subject(s) - mathematics , wavelet , galerkin method , stability (learning theory) , mathematical analysis , nonlinear schrödinger equation , nonlinear system , equation solving , scheme (mathematics) , function (biology) , schrödinger equation , partial differential equation , computer science , physics , quantum mechanics , artificial intelligence , machine learning , evolutionary biology , biology
A general implementation is presented for constructing a wavelet method for solving the nonlinear equation of Schr¨odinger. An explicit formula is derived which yields a stability in of the numerical solution. A simulation is elaborated to show the general behavior of the distribution function. Numerical results and comparison with classical algorithms are provided. This approach prove an attractive scheme for solving such equation.