Statistics – Computation
Scientific paper
Jan 2012
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2012geoji.188..253g&link_type=abstract
Geophysical Journal International, Volume 188, Issue 1, pp. 253-262.
Statistics
Computation
Numerical Solutions, Numerical Approximations And Analysis, Computational Seismology, Wave Propagation
Scientific paper
As the first step towards a general analysis of the stability of optimally accurate predictor-corrector (P-C) time domain discretized schemes for solving the elastic equation of motion, we analyze the stability of two P-C schemes for a 1-D homogeneous case. Letting Δt be the time step, h be the spatial grid interval, β be the velocity of seismic wave propagation and ? be the dimensionless Courant parameter, we find that each scheme has the following stability properties: stability for ?, instability for ?, stability for ? and instability for ?, where ?. We refer to the region ? as the second island of stability. The values of ?, ? and ? are scheme-dependent. The existence of a second island of stability in a numerical scheme for solving the wave equation has not, to our knowledge, been previously reported.
Geller Robert J.
Hirabayashi Nobuyasu
Mizutani Hiromitsu
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