Robin型边界阻尼波动方程的半离散一致指数稳定逼近

Semi-Discretized Approximation for Uniformly Exponential Stability of Wave Equation with Damped Robin Boundary

对一维Robin型边界阻尼波动方程构造了一个新的等距网格上的半离散有限差分格式,该格式没有数值粘性项,且可以保持系统的一致指数稳定性.通过引进一个新的辅助函数,利用Lyapunov函数方法证明了半离散格式的一致指数稳定性.数值实验验证了理论结果.

A new semi-discrete finite difference scheme on equidistant grids is proposed for one-dimensional wave equation with damped Robin boundary,which does not need any numerical viscosity terms and preserves the uniformly exponential stability of continuous syst em.The Lyapunov func tion met hod is adopted to prove the uniformly exponential stability of semi-discrete scheme by introducing a new auxiliary function.