Correct the code to have the answer: The temperature $u(x,y)$ corresponding to a rectangular plate comes from the Laplace equation:

$\frac{de{l}^{2}u(x,y)}{del{x}^2}+\frac{de{l}^{2}u(x,y)}{del{y}^2}=0$

Find the analytical and numeric solution from the equation with the next conditions: $u(0,y)=0,u_{2,y}=y,u(x,0)=0,$ and

$u(x,2)=0.$ Use a mesh $h=\frac{1}{2}.$ Find the solution using Maple.

SOLUTION:

$>$ restart;

$>$ with$($plots$)$;

multiple, odeplot, pareto, plotcompare, pointplot, pointplot$3$d$,$ polarplot, polygonplot, polygonplot$3$d$,$ polyhedra$\_$supported, polyhedraplot, rootlocus, semilogplot, setcolors, setoptions, setoptions$3$d$,$

shadebetween, spacecurve, sparsematrixplot, surfdata, textplot, textplot$3$d$,$ tubeplot$]$

$>h$:$=\frac{1}{2}$;

$h$:$=\frac{1}{2}$

$eq$:$=\frac{de{l}^2}{del{x}^2}u(x,y)+\frac{de{l}^2}{del{y}^2}u(x,y)=0$

$bcs$:$=\{u(0,y)=0,u(2,y)=y,u(x,0)=0,u(x,2)=0\}$

$nx$:$=2$

$ny$:$=2$

$>eq$ :$=$diff$(u(x,y),x,x)+$diff$(u(x,y),y,y)=0$;

$>bcs$:$=\{u(0,y)=0,u(2,y)=y,u(x,0)=0,u(x,2)=0\}$;

$>nx$:$=\frac{1}{h}$;$ny$:$=\frac{1}{h}$;

$I>$ mesh :$=[seq(i^{**}h,i=0..nx),$seq$(j^{**}h,j=0..ny)]$;

$>$sol:$=$pdsolve$([eq,bcs],$ numeric, time $=x,$ space $=y,$ mesh $=$ mesh $)$;

$h$:$=\frac{1}{2}$

$eq$:$=\frac{de{l}^2}{del{x}^2}u(x,y)+\frac{de{l}^2}{del{y}^2}u(x,y)=0$

$bcs$:$=\{u(0,y)=0,u(2,y)=y,u(x,0)=0,u(x,2)=0\}$

$nx$:$=2$

$ny$:$=2$

mesh :$=[0,\frac{1}{2},1,0,\frac{1}{2},1]$