diffusion_pde_test

diffusion_pde_test, a MATLAB code which calls diffusion_pde(), which solves the diffusion PDE dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using FTCS, the forward time difference, centered space difference method.

Licensing:

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

Related Data and codes:

diffusion_pde, a MATLAB code which solves the diffusion PDE dudt - mu * d2udx2 = 0 in one spatial dimension, with a constant diffusion coefficient mu, and periodic boundary conditions, using FTCS, the forward time difference, centered space difference method.

Source Code:

• diffusion_pde_test.m, calls all the tests.
• diffusion_pde_test.sh, runs all the tests.
• diffusion_pde_test.txt, the output file.

• diffusion_pde_ftcs.m, uses FTCS to solve the diffusion PDE.
• diffusion_pde_ode45.m, uses ode45() to solve the diffusion PDE.
• laplacian_interval.m, estimates the second derivative of a function of x whose values are given at equally spaced points.

• diffusion_pde_ftcs_initial.png, the initial condition.
• diffusion_pde_ftcs_final.png, the approximated solution at the final time.
• diffusion_pde_ftcs_conservation.png, the conserved quantity over time.
• diffusion_pde_ftcs.avi, an animation of the sequence of solutions.

• diffusion_pde_ode45_initial.png, the initial condition.
• diffusion_pde_ode45_final.png, the approximated solution at the final time.
• diffusion_pde_ode45.avi, an animation of the sequence of solutions.