On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
On error bounds for the Gautschi-type exponential integrator applied to oscillatory second-order differential equations
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DOI：
10.1007/s00211-005-0583-8
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发表时间：
2005-03
影响因子：
2.1
通讯作者：
Volker Grimm
中科院分区：
文献类型：
--
作者：
Volker Grimm
本文研究了一类二阶振动微分方程的数值方法，其中高频振动是由一个线性的时间和/或解相关的部分产生的。对于常线性部分，该方法允许二阶误差界与步长与频率的乘积无关，因此是一种长时间步长方法。大多数现实世界的问题不是这类问题，研究更一般的方程很重要。本文的分析表明，即使在时间和/或解决方案相关的线性部分的情况下，如果矩阵的平均位置进行评估，一个获得二阶误差界。
This paper studies a numerical method for second-order oscillatory differential equations in which high-frequency oscillations are generated by a linear time- and/or solution-dependent part. For constant linear part, it is known that the method allows second-order error bounds independent of the product of the step-size with the frequencies and is therefore a long-time-step method. Most real-world problems are not of that kind and it is important to study more general equations. The analysis in this paper shows that one obtains second-order error bounds even in the case of a time- and/or solution-dependent linear part if the matrix is evaluated at averaged positions.