Splitting methods in the numerical integration of non-autonomous dynamical systems
Splitting methods in the numerical integration of non-autonomous dynamical systems
复制标题
非自治动力系统数值积分中的分裂方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
A. Murua
中科院分区：
文献类型：
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作者：
S. Blanes;F. Casas;A. Murua
我们提出了一种方法，可以有效地解显式时变分块线性微分方程的时间积分，当某些偏微分方程先前在空间上离散时产生。第一阶段分析了相应自治问题的阶条件，构造了新的六阶方法。在第二阶段，通过遵循作者先前设计的程序，我们将方法推广到时间相关的情况下，这样就不会出现阶数减少。所得到的方案与以前可用的其他集成商相比具有优势。
We present a procedure leading to efficient splitting schemes for the time integration of explicitly time dependent partitioned linear differential equations arising when certain partial differential equations are previously discretized in space. In the first stage we analyze the order conditions of the corresponding autonomous problem and construct new 6th-order methods. In the second stage, by following a procedure previously designed by the authors, we generalize the methods to the time dependent case in such a way that no order reduction is present. The resulting schemes compare favorably with other integrators previously available.