Differential Equations Solutions 169

Differential Equations Solutions 169 - solution is shown in...

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Chapter 29 Solutions: Case Study: Elastoplastic Torsion: Twist and Stress CHALLENGE 29.1. A sample MATLAB program is available on the website. We can estimate the error in E ( u ) by computing estimates with fner and fner grids, using the fnest one as an approximation to truth. We expect the error in the estimates to drop by a Factor oF 4 each time the mesh size is halved (since the error is proportional to h 2 ), and that is what we observe. The mesh oF ±igure 29.1 produces an energy estimate with estimated error less than 0 . 1; the resulting
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Unformatted text preview: solution is shown in igure 29.2. CHALLENGE 29.2. We set up the Lagrangian Function L ( x, y, ) = ( x z 1 ) 2 + ( y z 2 ) 2 x 2 + y 2 1 ! , where the scalar is the Lagrange multiplier For the constraint. Setting the three partial derivatives to zero yields 2( x z 1 ) 2 x 2 = 0 , 2( y z 2 ) 2 y 2 = 0 , x 2 + y 2 1 = 0 . We conclude that x = 2 z 1 2 , (29.1) y = 2 z 2 2 , (29.2) 179...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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