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Summary

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 §D.2 above, convergence means that solutions of the FDS approach corresponding solutions of the PDE as $ T,X\to0$ .


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2015-05-22 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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