helmholtz_exact, a Python code which evaluates an exact formula for the solution of the Helmholtz equation, a sort of eigenvalue equation that can arise after separation of variables is a applied to the wave equation. This example considers a problem in which Z(x,y) represents the vertical deflection of the surface of a vibrating circular membrane such as a drumhead.
The formula relies on the evaluation of Bessel J functions and their zeros.
The information on this web page is distributed under the MIT license.
helmholtz_exact is available in a MATLAB version and an Octave version and a Python version.
python_exact, a Python code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).