I'm working on the Black-Scholes equation, but I'm pretty new to financial modeling. Right now, I am trying to understand the Black-Scholes PDE. I understand that the Black-Scholes equation is given by\begin{equation*}\frac{\partial C}{\partial t} + \frac{1}{2}\sigma^2 S^2\frac{\partial^2 C}{\partial S^2} + rS \frac{\partial C}{\partial S} - rC = 0\end{equation*}with initial condition\begin{equation*}C(S,T) = \max (S-K, 0)\end{equation*}and boundary conditions\begin{equation*}C(0,t) = 0 \hspace{35pt} C(S,t) \rightarrow S \text{ as } S \rightarrow \infty\end{equation*}and $C(S,t)$ is defined over $0 < S < \infty$, $0 \leq t \leq T$.This can be further transformed and simplified into a heat diffusion equation as described here. If we make the following change of variable\begin{equation*}u = e^{-r\tau}C \hspace{20pt} \text{ or } \hspace{20pt} C = ue^{r\tau}\end{equation*}and\begin{equation*}S = e^x \hspace{25pt} \text{ and }  \hspace{25pt} t = T- \tau \hspace{20pt} \end{equation*}we get the transformed heat equation\begin{equation*}\frac{\partial u}{\partial \tau} = \frac{\partial^2 u}{\partial x^2} + (k-1)\frac{\partial u}{\partial x} - ku\end{equation*}Where $k = \frac{2r}{\sigma^2}$. The following matlab code implements this. My question is, what exactly is the form of the boundary conditions for the the transformed equation? I can't seem to understand the parameters (related to the boundary conditions) given in the Matlab code. Any related literature would be highly appreciated. 
Boundary Conditions for the given PDE
pde;boundary conditions;parabolic pde