I was asked to implement, using the appropriate Green's function, the solution to the 2D heat equation on a rectangle:
$I_t=I_{xx}+I_{yy}$
with Neumann B.C. : $\overrightarrow{n}\cdot(\overrightarrow{\nabla}I)$
where $\overrightarrow{n}$ is the normal to the domain and $\overrightarrow{\nabla}I$ is the gradient of $I$
according to here, the Green's function for this problem is given by $H(t)\frac{1}{4\pi t}e^{-\frac{x^2+y^2}{4t}}$ where $H(t)$ is the heaviside function.
Is this Green's function applies for both Neumann and Dirichlet B.Cs?
if so, how do I take Neumann B.C. into consideration when solving for $I$.