Conserved quantities of some Hamiltonian wave equations after full discretization
Conserved quantities of some Hamiltonian wave equations after full discretization
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DOI：
10.1007/s00211-006-0680-3
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发表时间：
2006-04
影响因子：
2.1
通讯作者：
B. Cano
中科院分区：
文献类型：
--
作者：
B. Cano
哈密顿偏微分方程有一些不变量，这将是很好的保存与数值积分。本文主要研究非线性波动方程和薛定谔方程。在正则性和周期性的假设下，研究了对称空间离散化如何使空间离散化系统也有一些不变量或“近似”不变量很好地逼近连续不变量.我们猜想一些事实，这将解释良好的数值逼近后，他们的时间积分时，使用辛龙格库塔方法或对称线性多步法的二阶系统。
Hamiltonian PDEs have some invariant quantities, which would be good to conserve with the numerical integration. In this paper, we concentrate on the nonlinear wave and Schrödinger equations. Under hypotheses of regularity and periodicity, we study how a symmetric space discretization makes that the space discretized system also has some invariants or `nearly' invariants which well approximate the continuous ones. We conjecture some facts which would explain the good numerical approximation of them after time integration when using symplectic Runge-Kutta methods or symmetric linear multistep methods for second-order systems.