Can someone help me solve this non-homogeneous PDE (Poisson's equation)?
uxx + uyy = sin(x)sin(2y), 0 < x < pi, 0 < y < pi
with the conditions:
u(x,0) = sin(3x), u(x,pi) = 0, u(0,y) = 0, and u(pi,y) = sin(y)
Any help is greatly appreciated.
Can someone help me solve this non-homogeneous PDE (Poisson's equation)?
uxx + uyy = sin(x)sin(2y), 0 < x < pi, 0 < y < pi
with the conditions:
u(x,0) = sin(3x), u(x,pi) = 0, u(0,y) = 0, and u(pi,y) = sin(y)
Any help is greatly appreciated.
Let then .
We will try to find a function so that would solve the equation you want to ask. This would require . We also want therefore . We also want therefore . We also want therefore . We also want therefore .
Now we can find the solution. Solve subject to the boundary value problem . This is a standard exercise with seperation of variables. One you get the solution then the solution to the original problem would be .