A thin composite concrete slab can be represented using the PDE: $\frac{de{l}^2}{del{x}^2}+\frac{de{l}^2}{del{y}^2}-0\mathrm{.}3=0$

$(x,y)$ is defined in the domain: $0x2$ and $0y2\mathrm{.}4.$ The boundary conditions are given as: $(x,0)=1+x,(x,2\mathrm{.}4)=2,(0,y)=1,$ and $(2,y)=2.$

$2\mathrm{.}1$ Create a neat, labelled grid for Finite Difference $($FD$)$ analysis using divisions of $x=0\mathrm{.}5$ and $y=0\mathrm{.}6.$ Also, show the numbering for boundary conditions for each interior and boundary point.

$2\mathrm{.}2$ Generate the central difference equation for the given problem.

$2\mathrm{.}3$ Briefly explain the remaining steps to obtain the $$ values at the interior grid points of concrete slab.

$2\mathrm{.}4$ The specified boundary conditions are known as Dirichlet, describe how they differ from Neumann boundary conditions.

$2\mathrm{.}5$ Describe how the FD discretization in Q$2\mathrm{.}1$ leads to an estimation of the potential $()$ rather than the precise solution. Also, provide a suggestion on how this approximation can be improved.

$2\mathrm{.}6$ Provide the central difference equation if you decide to change the FD grid size to $5$ by $6,$ i$.$e$.,x=y=0\mathrm{.}4.($Hint: start from the final steps of the derivation performed in Q$2\mathrm{.}2).$