Solve the mixed boundary value problem for the Laplace equation 2 u = 0 in the rectangle

Solve the mixed boundary value problem for the Laplace equation ˆ‡²u = 0 in the rectangle in Fig. 458a (using the grid in Fig. 458b) and the boundary conditions u_x= 0 on the left edge, u_x= 3 on the right edge, u = x²on the lower edge, and u = x²- 1 on the upper edge.

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13 23 бх u, = I. 12 P32 3 P02 1.0 22 1.0 = 6 u = P, u = 3y³ P. P. 31 01 11 21 R 0.5 u = 0.375 P. 20 1.5 Tu = 0 Tu == 0 0.5 1.0 1.5