. The temperature distribution in the square region shown is governed by the Laplace equation, discussed in Chapter 10. The finite difference approximation to this equation yields a system of

algebraic equations given by where i is the number of the row and j is the column in which a grid point is located. For the nine points shown, obtain nine linear equations for determining the temperatures at these points. Solve this system by the Gauss-Seidel method. Note that the temperatures at the boundaries are given and are used in the equations for all the temperatures, except for the one at position number 5. Also, using the inv(A)command in MATLAB, solve this problem and compare the results with those obtained earlier.