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Summary of Well Posedness, Consistency, Stability, and Convergence

In summary, we have defined the following terms from the analysis of finite difference schemes for the linear shift-invariant case with constant sampling rates:

Finally, the Lax-Richtmyer equivalence theorem establishes that well posed + consistency + stability implies convergence, where, as defined in §L.2 above, convergence means that solutions of the FDS approach corresponding solutions of the PDE as $ T,X\to0$.


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[How to cite and copy this work] 
``Physical Audio Signal Processing for Virtual Musical Instruments and Digital Audio Effects'', by Julius O. Smith III, (December 2005 Edition).
Copyright © 2006-07-01 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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