论文标题
求解振荡性非线性哈密顿系统的功能保留能量的方法
Functionally-fitted energy-preserving methods for solving oscillatory nonlinear Hamiltonian systems
论文作者
论文摘要
在过去的几十年中，非线性振荡器的数值模拟受到了很多关注，许多研究人员一直关注解决振荡问题的数值方法的设计和分析。在本文中，从连续有限元方法的角度来看，我们提出和分析了新的能量保存功能拟合的方法，特别是用于解决具有固定频率的振动性非线性汉密尔顿系统的任意高阶的三角拟合方法。为了以广泛的方式实施这些新方法，它们被转变为一类连续阶段runge-kutta方法。本文伴随着有关振荡性哈密顿系统（例如FPU问题和非线性Schrödinger方程）的数值实验。数值结果证明了与文献中现有的高阶传播方法相比，我们的新方法的明显准确性和效率。
In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concerned with the design and analysis of numerical methods for solving oscillatory problems. In this paper, from the perspective of the continuous finite element method, we propose and analyze new energy-preserving functionally fitted methods, in particular trigonometrically fitted methods of an arbitrarily high order for solving oscillatory nonlinear Hamiltonian systems with a fixed frequency. To implement these new methods in a widespread way, they are transformed into a class of continuous-stage Runge--Kutta methods. This paper is accompanied by numerical experiments on oscillatory Hamiltonian systems such as the FPU problem and nonlinear Schrödinger equation. The numerical results demonstrate the remarkable accuracy and efficiency of our new methods compared with the existing high-order energy-preserving methods in the literature.
