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The steady$-$state distribution of

temperature on a heated plate can be modeled

by the Laplace equation,

$0=\frac{de{l}^{2}T}{del{x}^2}+\frac{de{l}^{2}T}{del{y}^2}$

If the plate is represented by a series of nodes

$($see the figure$),$ centered finite$-$divided

differences can be substituted for the second

derivatives, which results in a system of linear

algebraic equations. Use the Gauss$-$Seidel

method to solve for the temperatures of the

nodes in the figure. $[20$ pts$]$