Chebyshev Collocation Method for 2D Boundary Value Problems

a

8

b

1

3D plot

contour plot

Consider the 2D boundary value problem given by

2

∇

u=

u

xx

+

u

yy

=10sin[ax(y-b)]

, with boundary conditions

-1≤x,y≤1

and

u(x,y)=0

. You can set the values of

a

and

b

. Using this Demonstration, you can solve the PDE using the Chebyshev collocation method adapted for 2D problems. The solution is shown as either a 3D plot or a contour plot.