begin figure begin center leavevmode epsfbox diffusion absorb plot the heat at depths of 0 5 10 15 and 20 m image thumbnail plot the heat at depths of 0 5 10 15 and 20 m a line plot of the solution at a fixed point u 5 0 t examples and tests 1d heat transfer plotting the data result in the a graph graphs solution of a diffusion problem initial condition upper left 1 100 reduction of the small waves upper right 1 10 reduction of the long wave examples and tests laplace equation in a semi infinite rectangular domain laplace sol m image thumbnail diffusion with ftcs scheme unsteady convection diffusion reaction problem figure 4 amplification factors for small time steps begin figure begin center leavevmode epsfbox diffusion noflux image thumbnail diffusion with crank nicolson scheme solving the heat diffusion equation 1d pde in matlab figure 2 amplification factors for large time steps an image of the computed solution discretizing the 2d heat equation gifcreator me jyqlj examples and tests image thumbnail figure 12 solution of the stationary diffusion equation corresponding to a piecewise constant diffusion coefficient fs heat m fourier spectral method for heat equation u t u 0 x 1 with dirichlet neumann bcs using odd even extension to a periodic domain plot the heat at depths of 0 5 10 15 and 20 m fault scarp diffusion extended domain an image of the solution figure 3 amplification factors for time steps around the forward euler ility limit it is possible to choose from three diffe methods for solving two diffe pdes wave equation and diffusion equation there are several diffe the solution is somewhat sensitive to the choices of time step and spatial discretization if you make the time step too big the method is not le s lh4 googleusercontent com uyhk 80w5es uj1jhbqmcni aaaaaaaazt8 vnmzo tq0ik s691 nar 2520heat 2520equation gif pic 1d convection diffusion equation matlab tessshlo a png image of the solution image thumbnail 1d diffusion equation k just need help on implementation of ex 30 3 in matlab mit numerical methods for partial diffeail equations lecture 1 convection diffusion equation you 22 matlab plots initial condition and solution after time 1 when the waveform has advected once around the domain numerical solution by finite difference method for 1d heat or diffusion plot the heat at depths of 0 5 10 15 and 20 m