**JULIUS O. SMITH III
**

*Date:* July 21, 2004

It is known that the digital waveguide (DW) method for solving the
wave equation numerically on a grid can be manipulated into the form
of the standard finite-difference time-domain (FDTD) method (also
known as the ``leapfrog'' recursion). This paper derives a simple
rule for going in the other direction, that is, converting the state
variables of the FDTD recursion to corresponding wave variables in a
DW simulation. Since boundary conditions and initial values are more
intuitively transparent in the DW formulation, the simple means of
converting back and forth can be useful in initializing and
constructing boundaries for FDTD simulations.

- Introduction
- Ideal String Wave Equation

- State Transformations
- Examples
- Localized Displacement Excitations
- Localized Velocity Excitations
- More General Velocity Excitations
- Additive Inputs
- Physical Interpretation of

- State Space Formulation

- Computational Complexity
- Summary
- Future Work
- Bibliography
- About this document ...

Download wgfdtd.pdf

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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