| Author |
Comment/Response |
Dustin
|
 10/08/12 11:28am
I am trying to make a contour plot of the Laplace equation in polar coordinates on the wedge from 0 < theta < Pi/2
Will this work? Every time I run it, it says running and never does anything or gives an error. Just a constant running.
Nmax = 50;
\[Lambda] = Table[2 n - 1, {n, 1, Nmax}];
r[x_, y_] = Sqrt[x^2 + y^2];
\[Theta][x_, y_] = ArcTan[x, y];
f[\[Theta]_] = \[Theta];
B = Table[(1/(r[x, y]^{\[Lambda][[n]]}*Pi))*
Integrate[
f[\[Theta][x, y]]*Sin[\[Lambda][[n]]*\[Theta][x, y]], {x, 0,
1}, {y, 0, 1}], {n, 1, Nmax}];
u[r[x, y], \[Theta][x, y]] =
Sum[B[[n]]*Sin[\[Lambda][[n]]*\[Theta][x, y]]*
r[x, y]^{\[Lambda][[n]]}, {n, 1, Nmax}];
ContourPlot[u[r[,x], \[Theta][x,y]], {x, 0, 1}, {y, 0, 1},
PlotRange -> All, ColorFunction -> "Rainbow"]
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