Use Algorithm 12.5 to approximate the solution to the following partial differential
Chapter 12, Problem 12.4.1(choose chapter or problem)
Use Algorithm 12.5 to approximate the solution to the following partial differential equation (see the 0.5 0.5 1 D S1 S2 S1 x figure): x y2 u x (x, y) + y y2 u y (x, y) yu(x, y) = x, (x, y) D, u(x, 0.5) = 2x, 0 x 0.5, u(0, y) = 0, 0.5 y 1, y2 u x (x, y) cos 1 + y2 u y (x, y) cos 2 = 2 2 (y x) for (x, y) S2. Let M = 2; T1 have vertices (0, 0.5), (0.25, 0.75), (0, 1); and T2 have vertices (0, 0.5), (0.5, 0.5), and (0.25, 0.75).
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