For the grid in Fig. 456 compute the potential at the four internal points by Gauss and

Question:

For the grid in Fig. 456 compute the potential at the four internal points by Gauss and by 5 Gauss€“Seidel steps with starting values 100, 100, 100, 100 (showing the details of your work) if the boundary values on the edges are:

u = x⁴ on the lower edge, 81 - 54y² + y⁴ on the right, x⁴ - 54x² + 81 on the upper edge, y⁴ on the left. Verify the exact solution x⁴ - 6x²y² + y⁴ and determine the error.

3 P22 P12 2 P. P11 21 2 3.