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边界条件为控制函数的双曲方程的数值方法
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Abstract:
在这篇文章里，我们考虑源自于控制消振问题的双曲方程，由于它的边值条件是需求解的控制函数，导致它不同于通常的偏微分方程的定解问题。在没有关于初始位移和初始速度的任何假设下，给出了控制函数的解析形式，截取级数的前2(N + 1)项作为数值逼近解，获得了数值逼近的收敛速度，数值实验验证了理论结果。
In this paper, we are concerned with the development of numerical method for a class of hyperbolic equations, which are originated from the problem of vibration control and elimination in practice. Since its boundary condition is the control function which is needed to be solved, it is different from the ordinary initial value and boundary value problems of partial differential equations. Without any assumptions on initial displacement and initial velocity, the analytical form of the control function is given, and a numerical approximation solution is obtained by intercepting the first 2(N + 1) terms of the series, and a convergence rate of numerical approximation is analyzed. Numerical experiments confirm the theoretical results.
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