There is a rectangular plate whose edges are maintained at a certain temperature.
We are interested in finding the temperature at the interior points. Consider the
following diagram.
Approximations must be found for points to ; that is the temperature of the
intermediate points. Suppose that the temperature at an interior point is the
average of the temperatures of the four points surrounding it With this assumption, establish a system of equations, considering first the point
then the point etc. Rewrite the system so that all variables are on only one side of the equation.
Find the coefficient matrix and the augmented matrix. Observe the shape of the coefficient matrix diagonal band, symmetric, etc.
Solve the system using the Gauss, Jacobi, and GaussSeidel methods. Make a table and compare your results.
