fisher_pde_ftcs, a MATLAB code which estimates a solution of the Kolmogorov Petrovsky Piskonov Fisher partial differential equation (PDE) ut=uxx+u*(1-u), using the forward time centered space (FTCS) method, with an oscillating Dirichlet condition on the left, and a zero Neumann condition on the right.
The use of the explicit FTCS method requires that the time steps be small; otherwise the computed solution will become unstable.
The information on this web page is distributed under the MIT license.
fisher_pde_ftcs is available in a MATLAB version.
advection_pde, a MATLAB code which solves the advection PDE dudt + c * dudx = 0 in one spatial dimension and time, with a constant velocity c, and periodic boundary conditions, using the forward time centered space (FTCS) difference method.
allen_cahn_pde, a MATLAB code which sets up and solves the Allen-Cahn reaction-diffusion system of partial differential equations (PDE) du/dt = nu * uxx - u * (u^2-1) / (2*xi) in 1 space dimension and time.
diffusion_pde, a MATLAB code which solves the diffusion partial differential equation (PDE) dudt - mu * d2udx2 = 0 in one spatial dimension and time, with a constant diffusion coefficient mu, and periodic boundary conditions, using the forward time centered space (FTCS) difference method.
fd1d_advection_diffusion_steady, a MATLAB code which applies the finite difference method to solve the steady advection diffusion equation v*ux-k*uxx=0 in one spatial dimension, with constant velocity v and diffusivity k.
fd1d_advection_ftcs, a MATLAB code which applies the finite difference method (FDM) to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the forward time, centered space (FTCS) difference method.
fd1d_advection_lax, a MATLAB code which applies the finite difference method to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the Lax method to treat the time derivative.
fd1d_advection_lax_wendroff, a MATLAB code which applies the finite difference method to solve the time-dependent advection equation ut = - c * ux in one spatial dimension, with a constant velocity, using the Lax-Wendroff method to treat the time derivative.
fd1d_burgers_lax, a MATLAB code which applies the finite difference method and the Lax-Wendroff method to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
fd1d_burgers_leap, a MATLAB code which applies the finite difference method and the leapfrog approach to solve the non-viscous time-dependent Burgers equation in one spatial dimension.
fd1d_heat_explicit, a MATLAB code which uses the finite difference method and explicit time stepping to solve the time dependent heat equation in 1D.
fd1d_heat_implicit, a MATLAB code which uses the finite difference method and implicit time stepping to solve the time dependent heat equation in 1D.
fd1d_wave, a MATLAB code which applies the finite difference method to solve the time-dependent wave equation utt = c * uxx in one spatial dimension.