Consider the steady state temperature distribu$-$

tion on a rectangular plate discretized by a $65$

grid with $x=0\mathrm{.}1m$ and $y=0\mathrm{.}2m$ as shown

in the figure. The boundary conditions are also

provided in the figure.

a$)$ Solve for the temperature values at the $(i,j)=$

$(2,2)$ and $(3,2)$ grid points using the Gauss$-$

Seidel method at the first iteration. Take

the initial guess as $20C.$ Show all of your

calculations clearly.

b$)$ Employ the line Gauss$-$Seidel method for the

$i=2$ grid line. Write down the coeffi$-$

cient matrix and the right$-$hand side

vector with the exact numerical val$-$

ues.