Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs
Backward error analysis for multisymplectic discretizations of Hamiltonian PDEs
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DOI：
10.1016/j.matcom.2005.01.006
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发表时间：
2004-12
期刊：
影响因子：
--
通讯作者：
A. Islas;C. Schober
中科院分区：
文献类型：
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作者：
A. Islas;C. Schober
最近发展的几个多辛格式的哈密顿偏微分方程已被证明保持相关的局部守恒律和约束很好地在长时间的数值模拟。偏微分方程的向后误差分析，或修正方程的方法，是研究离散化的定性行为的一种有用的技术，并提供了深入了解该计划的保存属性。在本文中，我们提出了一个向后误差分析偏微分方程离散，特别是多辛盒计划的非线性薛定谔方程。我们证明了相应的修正微分方程也是多辛的，并导出了修正的守恒律，数值解满足高阶。数值上验证了修正后的局部守恒律的高阶保持性。
Several recently developed multisymplectic schemes for Hamiltonian PDEs have been shown to preserve associated local conservation laws and constraints very well in long time numerical simulations. Backward error analysis for PDEs, or the method of modified equations, is a useful technique for studying the qualitative behavior of a discretization and provides insight into the preservation properties of the scheme. In this paper we initiate a backward error analysis for PDE discretizations, in particular of multisymplectic box schemes for the nonlinear Schrödinger equation. We show that the associated modified differential equations are also multisymplectic and derive the modified conservation laws which are satisfied to higher order by the numerical solution. Higher order preservation of the modified local conservation laws is verified numerically.