Finite Difference Schemes for the Wave Equation

In this appendix, we reexamine the finite difference schemes corresponding to the waveguide meshes discussed in Chapter 4, in the special case for which the underlying model problem is lossless, source-free and does not exhibit any material parameter variation. In this case, these finite difference schemes will solve the wave equation, given by

in either (2+1)D or (3+1)D, depending on the type of mesh. Here, is the

- Von Neumann Analysis of Difference Schemes

- Finite Difference Schemes for the (2+1)D Wave Equation
- The Rectilinear Scheme
- The Interpolated Rectilinear Scheme
- The Triangular Scheme
- The Hexagonal Scheme
- A Fourth-order Scheme

- Finite Difference Schemes for the (3+1)D Wave Equation

Stefan Bilbao 2002-01-22