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Substituting finite difference approximation (FDA)
into the wave equation
gives
Time Update:
Let
(speed of sound along the string).
In practice, we typically normalize such that
 Higher order wave equations yield more terms of the form
frequencydependent losses and/or dispersion
characteristics are introduced into the FDA:
 Linear differential equations with constant coefficients give rise to some
linear, timeinvariant discretetime system via the FDA
 Linear, timeinvariant, ``filtered waveguide'' case:
 More general linear, timeinvariant case
 Nonlinear example:
 Timevarying example:
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