(Solved): (Q3) : Given the two dimensional heat equation as: \( \frac{\partial h}{\partial t}=c\left[\frac{\p ...

(Q3) : Given the two dimensional heat equation as: \( \frac{\partial h}{\partial t}=c\left[\frac{\partial^{2} h}{\partial^{2} x}+\frac{\partial^{2} h}{\partial^{2} y}\right] \), where \( c \) is a constant number. For the discretization of the time and spatial domains, assume that: a) \( \Delta x=\Delta y \). b) forward difference for the time derivative term and c) central difference for the spatial derivative terms Set up the discretized \( h \) so that on can use numerical methods to determine the time evolution of \( h \).