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# hw6_09 - EP 471 Homework#6 Elliptic PDEs Each problem is...

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04/12/09 EP 471 – Homework #6: Elliptic PDEs Each problem is equally weighted: (1) Consider the following elliptic partial differential equation: 2 2 2 2 2 2 = + x u y u x u , Solve this problem over the unit square, 1 0 x , 1 0 y , subject to u = 0 on all boundaries. Approximate all derivatives with centrally-differenced expressions. You may use either a direct solution (simultaneous system of equations) or an iterative solution. Find the peak value of u within the domain. (2) In Exercises 16 and 17, we looked at solutions to Laplace’s Equation in a rectangular plate over the domain m 5 . 0 0 ; m 1 0 y x with the temperature equal to zero ° C along three edges and a non-zero temperature of 100 ° C on one edge. Suppose we modify this problem in two ways: we’ll incorporate a spatially-dependent heat source to turn Laplace’s Equation into Poisson’s Equation, and we’ll incorporate convective boundary conditions along the three edges that were previously specified as zero temperature boundaries.

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hw6_09 - EP 471 Homework#6 Elliptic PDEs Each problem is...

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