Approximate the solution to the partial differential equation d 2 u d 2 u 2 2 5n 5n -
Chapter 12, Problem 3(choose chapter or problem)
Approximate the solution to the partial differential equation d 2 u d 2 u 2 2 5n 5n - M.Stt u(x,y) =-257T sinx siny, 0 < x, y < 0.4, 9x2 9;y2 2 2 subject to the Dirichlet boundary condition u(x,y) - 0, using theFinite-ElementAlgorithm 12.5 with the elements given in the accompanying figure. Compare the approximate solution to the actual solution, . 5jt . 5n u(x, y) = sin x sin at the interior vertices and at the points (0.125, 0.125), (0.125, 0.25), (0.25, 0.125), and (0.25, 0.25). 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4
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