2009501436_&igrave;œ&nbsp;&ecirc;&acute;‘&igrave;„&nbsp;_hw#8

# 2009501436_ìœ ê´‘ì„ _hw#8

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Unformatted text preview: Home Work. #6 1. Part I 1) Find the exact solution to (0.1) for this f(x). 2) Divide the interval [0, 1] into two sub-intervals [0, h] and [h, h+H], where h+H = 1. Using the notation and definitions beginning on page 299 in your text, write down formulas for the load vector F in terms of f using a midpoint approximation for f(x) (see formulas 23-24). 3) Using the functions ' j , j = 0, 1, 2, the Global matrix K constructed beginning on page 299 in your text, and your vector F from question (2), find the coefficients U 0 and U 1 (the boundary condition implies U 2 = 0) for two cases: h = H = 1/2, and for h = 1/3 and H = 2/3. 4) For h = H = 1/2, U 0 is an approximation for u(0) and U 1 is an approximation for u(1/2). Compare to the values for your exact solution. For h = 1/3, H = 2/3, what values do U 0 and U 1 approximate? Compare to the values for your exact solution. Is this better or worse than h = H = 1/2? 1) solution- 1 4, 0 3 ( ) 1 1, 1 3 x f x x = 2 2 2 (0 1/ 3) 4 " 1 1 ( 1/ 3) (1/ 3 1) 2 x ax b x u u x cx d x - + + - = = --- + + < B.CL 2 2 2 1 (1) : 2 '(0) : 1 1 1 1 1 1 ( ) ( ) : ( ) ( ) 2( )...
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## This note was uploaded on 12/10/2009 for the course ME master taught by Professor Mon during the Spring '09 term at Hanyang University.

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2009501436_ìœ ê´‘ì„ _hw#8

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