minimal_surface_exact

minimal_surface_exact, an Octave code which evaluates exact solutions u(x,y) to the minimal surface equation: (1+Ux^2) Uyy - 2 Ux Uy Uxy + (1+Uy^2) Uxx = 0.

Four exact solutions are provided here, the plane, the helicoid, the catenoid, and Scherk's function.

Licensing:

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

Languages:

minimal_surface_exact is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

minimal_surface_exact_test

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

Reference:

1. John D Cook,
   Closed-form minimal surface solutions,
   https://www.johndcook.com/blog/2025/03/31/minimal-surface-solutions/
   Posted 31 March 2025.

Source Code:

• minimal_surface_linear_exact.m, returns the exact solution and derivatives for the linear case.
• minimal_surface_linear_residual.m, returns the residual for the linear case.
• minimal_surface_helicoid_exact.m, returns the exact solution and derivatives for the helicoid case.
• minimal_surface_helicoid_residual.m, returns the residual for the helicoid case.
• minimal_surface_catenoid_exact.m, returns the exact solution and derivatives for the catenoid case.
• minimal_surface_catenoid_residual.m, returns the residual for the catenoid case.
• minimal_surface_scherk_exact.m, returns the exact solution and derivatives for the Scherk case.
• minimal_surface_scherk_residual.m, returns the residual for the Scherk case.