How would i go about coding this Calculate the temperature distribution across a metal plate using a finite difference method.

Use finite central difference.

Assume steady conduction and that there is no heat conduction in the z$-$direction.

The plate is $2\mathrm{.}5m$ by $2\mathrm{.}5m,$ use an interval size of $0\mathrm{.}125$

The boundary conditions are

Wi

$T_{\text{l}\text{e}\text{f}\text{t}}=50c,T_{\text{t}\text{o}\text{p}}=20C,T_{\text{r}\text{i}\text{g}\text{h}\text{t}}=20c,T_{\text{b}\text{o}\text{t}\text{t}\text{o}\text{m}}=100C$

Make sure your output is in kelvin

Function $?$

function $[$T$,$ gridx,gridy, A$,$ b$]=$ heat$\_$conduction$($Tboundary$,$ Lx$,$ Ly$,$ dx$)$

$\%$ extract boundary conditions

Tleft $=$ Tboundary$(1)$;

Ttop $=$ Tboundary$(2)$;

Tright $=$ Tboundary$(3)$;

Tbottom $=$ Tboundary$(4)$;

$\%$ calc number of intervals in $x$ and $y$ direction

$\%$ setup grid of points in a vector of gridx and grid $y$

$\%$ create adjacency matrix

$A=$zeros$(n**m)$;

for $i=1$:$1$:$n**m$

for $j=1$:$1$:$n**m$

$\%$ set diagnonals of $A$ to $-4$

$\%$ calc distance between two of the grid points

$\%$ if distance is less than $dx,$ set A element to $1$

end

end

$\%$ apply boundary conditions

$\%$ cycle through each point to determine the boundary condition it is in

if $\%$bottom left corner

elseif $\%$ bottom right corner

elseif $\%$top left corner

All of this without a memory error please