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Let us now solve the diffusion equation in 2d using the finite difference technique discussed above.
We seek the solution of Eq. (214) in the region and
, subject to the following initial condition at :
The boundary conditions are simply
.
Figure 74:
Diffusion in two dimensions.
Numerical calculation performed using
,
, and . Density plots of are shown at
(topleft), (topright), (middleleft),
(middleright), (bottomleft), and (bottomright).

Figure 74 shows the evolution of for a calculation performed
with the previously listed 2d diffusion equation solver
using ,
, and .
Next: 3d problems
Up: The diffusion equation
Previous: An example 2d diffusion
Richard Fitzpatrick
20060329