Nonlinear systems with periodic variations of nonlinearity and/or dispersion occur in a
variety of physical problems and engineering applications. The mathematical concept of …

This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

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 …

This paper develops a formalism for the design of conserving time-integration schemes for
Hamiltonian systems with symmetry. The main result is that, through the introduction of a …

A split-step method is used to discretize the time variable for the numerical solution of the
nonlinear Schrödinger equation. The space variable is discretized by means of a finite …

We study the application of Runge-Kutta schemes to Hamiltonian systems of ordinary
differential equations. We investigate which schemes possess the canonical property of the …

We approximate the solutions of an initial-and boundary-value problem for nonlinear
Schrödinger equations (with emphasis on the 'cubic'nonlinearity) by two fully discrete finite …

In this paper, we study the unconditional convergence and error estimates of a Galerkin-
mixed FEM with the linearized semi-implicit Euler scheme for the equations of …

We present a new numerical scheme for nonlinear Schrödinger type equations. The scheme
conserves the energy and charge of the systems and it is linearly implicit. Numerical …

In this paper, we study linearized Crank–Nicolson Galerkin FEMs for a generalized
nonlinear Schrödinger equation. We present the optimal L^ 2 L 2 error estimate without any …