Absorbing Boundary

An Absorbing boundary is the most complicated.

• Since fixed boundaries for the diffusion equation already ``absorb'' or remove mass from the system, absorbing boundaries are redundant and have not been implemented for the diffusion equation.
• For the classical wave equation, we set the first grid point of the right-traveling wave or last grid point of the left-traveling wave equal to zero and let the propagation algorithm carry these zeros into the medium.
• Schrödinger wavefunctions are absorbed by adding extra grid points outside the medium where N is the number of grid points displayed on the screen. These points are given a very small absorption coefficient so that the wave is slowly attenuated after it crosses the boundary. In addition, the potential for these extra points is chosen to be that of the potential at the last point inside the medium, so that there is little discontinuity. This method works for all energies and typically results in an unwanted reflection of less than .
• Absorbing boundary conditions have not been implemented for Klein-Gordon type equations, although a scheme similar to that employed for the Schrödinger equation would not be difficult to code.