摘要
In this paper,we investigate the stability for a finite harmonic lattice under a certain class of boundary conditions.A rigorous eigenvalue study clarifies that the invalidity of Fourier modes as the basis results in the deficiency of standard reflection coefficient approach for stability analysis.In a certain parameter range,unstable surface modes exist in the form of exponential decay in space,and exponential growth in time.An approximate eigen-polynomial is proposed to ease the stability analysis.Moreover,the eigenvalues with small positive real part quantitatively explain the long time instability in wave propagation computations.Numerical results verify the analysis.
基金
supported in part by NSFC under contract number 10872004
National Basic Research Program of China under contract number 2007CB814800
the China Ministry of Education under contract numbers NCET-06-0011 and 200800010013.
