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Difference Equations
(Finite Difference Schemes)
There are many methods for converting
ODEs
and
PDEs
to
difference equations
For example, we'll use a very simple, order-preserving method which
replaces each derivative with a
finite difference
:
for sufficiently small
(the
sampling interval
)
This is formally known as the
backward difference
for approximating differentiation
We'll look a few others as well
Subsections
Difference Equation for a Force-Driven Mass
Replacing Backward-Difference by Forward-Difference
Explicit and Implicit Finite Difference Schemes
Semi-Implicit Finite Difference Schemes
Explicit Finite Difference Schemes as
Digital Filters
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Download
ReviewPM.pdf
Download
ReviewPM_2up.pdf
Download
ReviewPM_4up.pdf
``
Review of Physical Signal Models
'', by
Julius O. Smith III
, (From Lecture Overheads,
Music 420
).
Copyright ©
2020-06-27
by
Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),
Stanford University
[Automatic-links disclaimer]