On second-order differential equations with highly oscillatory forcing terms
On second-order differential equations with highly oscillatory forcing terms
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DOI：
10.1098/rspa.2009.0481
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发表时间：
2010-06
期刊：
影响因子：
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通讯作者：
M. Condon;A. Deaño;A. Iserles
中科院分区：
文献类型：
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作者：
M. Condon;A. Deaño;A. Iserles
我们提出了一种方法来有效地计算具有高振荡强迫项的常微分方程（ODE）系统的解决方案。这种方法是基于渐近展开的振荡参数的逆幂，并具有两个基本的优势，相对于标准的数值常微分方程求解器：第一，当系统是高度振荡的数值解的建设是更有效的，第二，计算的成本基本上是独立的振荡参数。数值例子提供，具有货车德尔波尔和Duffing振荡器和激励的问题，在电子工程。
We present a method to compute efficiently solutions of systems of ordinary differential equations (ODEs) that possess highly oscillatory forcing terms. This approach is based on asymptotic expansions in inverse powers of the oscillatory parameter, and features two fundamental advantages with respect to standard numerical ODE solvers: first, the construction of the numerical solution is more efficient when the system is highly oscillatory, and, second, the cost of the computation is essentially independent of the oscillatory parameter. Numerical examples are provided, featuring the Van der Pol and Duffing oscillators and motivated by problems in electronic engineering.