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Let us now solve Poisson's equation in one dimension, with mixed boundary conditions,
using the finite difference technique discussed above. We seek the
solution of

(142) 
in the region , with
. The boundary conditions
at and take the mixed form specified in Eqs. (132) and
(133). Of course, we can solve this problem analytically. In fact,

(143) 
where
Figure 62 shows a comparison between the analytic and finite difference
solutions for . It can be seen that the finite difference solution mirrors
the analytic solution almost exactly.
Figure 62:
Solution of Poisson's equation in one dimension with , , ,
, , , and . The dotted curve (obscured)
shows the analytic solution, whereas the open triangles show the finite difference
solution for .

Next: 2d problem with Dirichlet
Up: Poisson's equation
Previous: An example 1d Poisson
Richard Fitzpatrick
20060329