ﻻ يوجد ملخص باللغة العربية
In this paper, we analyse a new exponential-type integrator for the nonlinear cubic Schrodinger equation on the $d$ dimensional torus $mathbb T^d$. The scheme has recently also been derived in a wider context of decorated trees in [Y. Bruned and K. Schratz, arXiv:2005.01649]. It is explicit and efficient to implement. Here, we present an alternative derivation, and we give a rigorous error analysis. In particular, we prove second-order convergence in $H^gamma(mathbb T^d)$ for initial data in $H^{gamma+2}(mathbb T^d)$ for any $gamma > d/2$. This improves the previous work in [Knoller, A. Ostermann, and K. Schratz, SIAM J. Numer. Anal. 57 (2019), 1967-1986]. The design of the scheme is based on a new method to approximate the nonlinear frequency interaction. This allows us to deal with the complex resonance structure in arbitrary dimensions. Numerical experiments that are in line with the theoretical result complement this work.
For the solution of the cubic nonlinear Schrodinger equation in one space dimension, we propose and analyse a fully discrete low-regularity integrator. The scheme is explicit and can easily be implemented using the fast Fourier transform with a compl
A novel class of high-order linearly implicit energy-preserving exponential integrators are proposed for the nonlinear Schrodinger equation. We firstly done that the original equation is reformulated into a new form with a modified quadratic energy b
Recent theoretical and experimental advances show that the inertia of magnetization emerges at sub-picoseconds and contributes to the ultrafast magnetization dynamics which cannot be captured intrinsically by the LLG equation. Therefore, as a general
In this paper, a family of arbitrarily high-order structure-preserving exponential Runge-Kutta methods are developed for the nonlinear Schrodinger equation by combining the scalar auxiliary variable approach with the exponential Runge-Kutta method. B
Many problems encountered in plasma physics require a description by kinetic equations, which are posed in an up to six-dimensional phase space. A direct discretization of this phase space, often called the Eulerian approach, has many advantages but