一维边界阻尼波动方程指数稳定的半离散有限差分一致逼近格式

A Uniformly Approximated Semi-discretized Finite Difference Scheme for Exponential Stability of 1D Wave Equation with Damped Boundary

通过在时间方向引入一个平均算子,对一维边界阻尼波动方程构造了一个等距网格上的半离散有限差分格式.利用离散乘子法,证明了对偶系统半离散格式的一致可观测不等式,进而证明了原系统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 semi-discretized finite difference scheme on equidistant grids is proposed for 1D wave equation with damped boundary by introducing an average operator in time direction. The discretized multiplier method is adopted to prove the uniformly observable inequality of semi-discretized scheme for conjugate system. The uniformly exponential stability of semi-discretized scheme for original system is demonstrated further. A numerical experiment verifies the theoretical results.