helmholtz_exact

helmholtz_exact, a MATLAB 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.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

helmholtz_exact is available in a MATLAB version.

Related Data and codes:

helmholtz_exact_test

besselzero, a MATLAB code which computes zeros of Bessel j or y functions, by Greg van Winckel and Jason Nicholson.

matlab_exact, a MATLAB code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).

Reference:

• Milton Abramowitz, Irene Stegun,
  Handbook of Mathematical Functions,
  National Bureau of Standards, 1964,
  ISBN: 0-486-61272-4,
  LC: QA47.A34.

Source Code:

• besselzero.m, evaluates zeros of the Bessel J and Y functions.
• helmholtz_exact.m, evaluates an exact solution of the Helmholtz equation.