I am having a bit of trouble solving the 2D Laplace Equation $$\nabla^2u(y,z) = 0$$ with 2 BCs being
- $\left.\dfrac{\partial u}{\partial y}\right|_{y=0} = 0$
- $u\left(y=\frac{h}{2},z\right) = c\sin^2kz$
for a constant $c\neq0$.In previous mathematics and engineering classes, we have used separation of variables to solve the 2D Laplace equation, which resulted in sinusoidal solutions for one of the variables, and usually the problem was constructed such that at least one BC was periodic (first power) so that a matching solution could be found. How do I go about solving the Laplace equation for a sine-squared boundary?
Thanks!