On systems of differential equations with extrinsic oscillation
On systems of differential equations with extrinsic oscillation
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DOI：
10.3934/dcds.2010.28.1345
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发表时间：
2010-06
影响因子：
1.1
通讯作者：
M. Condon;A. Deaño;A. Iserles
中科院分区：
文献类型：
--
作者：
M. Condon;A. Deaño;A. Iserles
我们提出了一个有效的离散化的非线性微分方程系统的高振荡扰动的数值方案。该方法是上级标准的常微分方程数值求解器中存在的高频强迫项，是基于渐近展开的解的振荡参数$\omega$的逆幂，具有调制的傅立叶级数的展开系数。数值稳定性分析和数值算例。
We present a numerical scheme for an efficient discretization of nonlinear systems of differential equations subject to highly oscillatory perturbations. This method is superior to standard ODE numerical solvers in the presence of high frequency forcing terms, and is based on asymptotic expansions of the solution in inverse powers of the oscillatory parameter $\omega$, featuring modulated Fourier series in the expansion coefficients. Analysis of numerical stability and numerical examples are included.