Spatial manifestations of order reduction in Runge–Kutta methods for initial boundary value problems
Spatial manifestations of order reduction in Runge–Kutta methods for initial boundary value problems
复制标题
初始边值问题龙格-库塔方法降阶的空间表现
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
Dong Zhou
中科院分区：
文献类型：
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作者：
R. Rosales;Benjamin Seibold;D. Shirokoff;Dong Zhou
研究了高阶Runge-Kutta方法求解时步初边值问题时降阶的空间表现。对于这样的IBVP，出现的几何结构没有一个类似的ODE IVP：边界层出现，引起的内部和边界处的近似误差之间的不匹配。为了理解这些边界层，进行了分析的模式的数值方案，这解释了在何种情况下，边界层持续了许多时间步长。在此基础上，研究了两种降阶方法：第一，在Butcher表上增加一个新的条件，称为弱阶，它与对角隐式Runge-Kutta格式相容;第二，分析了修正边界条件对边界层理论的影响。
This paper studies the spatial manifestations of order reduction that occur when time-stepping initial-boundary-value problems (IBVPs) with high-order Runge-Kutta methods. For such IBVPs, geometric structures arise that do not have an analog in ODE IVPs: boundary layers appear, induced by a mismatch between the approximation error in the interior and at the boundaries. To understand those boundary layers, an analysis of the modes of the numerical scheme is conducted, which explains under which circumstances boundary layers persist over many time steps. Based on this, two remedies to order reduction are studied: first, a new condition on the Butcher tableau, called weak stage order, that is compatible with diagonally implicit Runge-Kutta schemes; and second, the impact of modified boundary conditions on the boundary layer theory is analyzed.
具有高弱阶段顺序的 DIRK 方案
DOI：
10.1007/978-3-030-39647-3_36
发表时间：
2020
期刊：
Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering. Springer.
影响因子：
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作者：
Ketcheson, D.;Seibold, B.;Shirokoff, D.;Zhou, D.
通讯作者：
Zhou, D.