Suppose we want to simulate one direction in an *acoustic space*
in which the air is described by the second-order wave equation

where is particle velocity of the air relative to equilibrium.

- This is the familiar 1-D wave equation, with wave speed given by
- for air (``adiabatic gas constant''),
- is ambient pressure, and
- is mass density.

- The same equation holds also for pressure and density , all with the same wave speed .

Let's ``digitize'' this wave equation to create a
*finite difference scheme* (FDS).

- Second-Order Finite Difference Scheme
- Time-Space Grid of Second-Order FDS
- A Peek at Stability of Finite Difference Schemes
- Von Neumann Analysis
- Problems with FDS

Download NumericalInt.pdf

Download NumericalInt_2up.pdf

Download NumericalInt_4up.pdf

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

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