Rectangular Pipe Example
A volume V is bounded by |x|= b and y = 0 and y = a. The electrostatic potential on surfaces are given by f(b,y)=f(-b,y)= V and f(x,0) = f(x,a) = a.
The solution is given by (Choosing a = b = 1 and V =1). (Here we add only first 500 terms of the series, and hope for the best. Notice that the graph is very accurate near x = 0, but not so accurate near x = b and x=-b.)
Open Pipe Example
A volume V is bounded by x= 0 and x = a and y = 0. The electrostatic potential on surfaces are given by f(0,y)=f(a,y)= 0 and f(x,0) = V.
The solution is given by (Choosing a = 1 and V =1).
Created by Mathematica (February 13, 2007)