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Unformatted text preview: 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 x , 1 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 Laplaces Equation in a rectangular plate over the domain m 5 . ; m 1 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: well incorporate a spatially-dependent heat source to turn Laplaces Equation into Poissons Equation, and well incorporate convective boundary conditions along the three edges...
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This note was uploaded on 01/30/2012 for the course ENGINEERIN 471 taught by Professor Witt during the Spring '08 term at Wisconsin.
- Spring '08