octave_exact, an Octave code which evaluates exact solutions to a few selected examples of ordinary differential equations (ODE) and partial differential equations (PDE).
These exact solutions can be used to test out the correctness of a solution algorithm.
The information on this web page is distributed under the MIT license.
octave_exact is available in a C version and a C++ version and a Fortran77 version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.
biharmonic_exact, an Octave code which evaluates exact solutions w(x,y) to the biharmonic equation del^2 w = 0 or wxxxx + 2 wxxyy + wyyyy = 0
burgers_exact, an Octave code which evaluates exact solutions of time-dependent 1D viscous Burgers equation.
fisher_exact, an Octave code which returns an exact solution of the Kolmogorov Petrovsky Piskonov Fisher partial differential equation (PDE) ut=uxx+u*(1-u).
flame_exact, an Octave code which returns the exact solution of an ordinary differential equation (ODE) which models the growth of a ball of flame in a combustion process. The exact solution is defined in terms of the Lambert W function.
helmholtz_exact, an Octave 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.
kdv_exact, an Octave code which evaluates an exact solution of the Korteweg-deVries (KdV) partial differential equation (PDE).
lindberg_exact, an Octave code which evaluates the exact solution of the Lindberg ordinary differential equations (ODE), a system that is extremely difficult to solve accurately.
logistic_exact, an Octave code which evaluates an exact solution of the logistic equation, an ordinary differential equation (ODE) which models population growth in the face of a limited carrying capacity.
navier_stokes_2d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 2D.
navier_stokes_3d_exact, an Octave code which evaluates an exact solution to the incompressible time-dependent Navier-Stokes equations (NSE) over an arbitrary domain in 3D.
pendulum_nonlinear_exact, an Octave code which evaluates an exact formula for the solution of the the ordinary differential equations (ODE) that represent the behavior of a nonlinear pendulum of length L under a gravitational force of strength G.
porous_medium_exact, an Octave code which returns an exact solution of the porous medium equation (PME), dudt=Del^2(u^m), a partial differential equation (PDE) related to the diffusion equation, based on the Barenblatt solution.
sine_gordon_exact, an Octave code which returns an exact solution of the Sine-Gordon equation, a partial differential equation (PDE) of the form uxy=sin(u).
spiral_exact, an Octave code which computes a 2D velocity vector field that is an exact solution of the continuity equation.
stokes_2d_exact, an Octave code which evaluates exact solutions to the incompressible steady Stokes equations over the unit square in 2D.