TY - JOUR
T1 - Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach
AU - Shaoqiang Tang & Ming Fang
JO - Communications in Computational Physics
VL - 1
SP - 143
EP - 158
PY - 2010
DA - 2010/08
SN - 8
DO - http://doi.org/10.4208/cicp.2009.09.065
UR - https://global-sci.org/intro/article_detail/cicp/7566.html
KW - 
AB - <p style="text-align: justify;">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.</p>