In this paper, we begin with the nonlinear Schrödinger/Gross–Pitaevskii equation
(NLSE/GPE) for modeling Bose–Einstein condensation (BEC) and nonlinear optics as well …

Nonlinear evolution equations are widely used to describe nonlinear phenomena in natural
and social sciences. However, they are usually quite difficult to solve in most instances. This …

Heat transfer processes in a photovoltaic (PV) silicon solar panel are simulated under
standard circumstances. A model containing an intricate treatment of the incoming solar …

Due to the difficulty in obtaining the a priori estimate, it is very hard to establish the optimal
point-wise error bound of a finite difference scheme for solving a nonlinear partial differential …

In this paper, we present a finite difference scheme for the triple-coupled Schrödinger
equations (T-CNLS) in optics. The T-CNLS is approximated by Crank-Nicolson scheme in …

In this paper, we study the analytical properties and the numerical methods for the
Bogoliubov-de Gennes equations (BdGEs) describing the elementary excitation of Bose …

This article proposes an advanced algorithm for the numerical solution of a coupled
nonlinear Schrödinger equations system describing the evolution of a high-power …

Two-grid algorithms based on two conservative and implicit finite element methods are
studied for two-dimensional nonlinear Schrödinger equation with wave operator. The …

A conservative two-grid mixed finite element scheme is presented for two-dimensional
nonlinear Schrödinger equation. One Newton iteration is applied on the fine grid to linearize …

A new two-grid finite element scheme is presented for two-dimensional nonlinear
Schrödinger equation. One Newton iteration is applied on the fine grid to linearize the …