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Review1A_98F

# Review1A_98F - Partial Solutions of Review Problems for...

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Partial Solutions of Review Problems for Midterm Examination MEAM501, Fall 1998 1. Weighted Residual Method Introducing an arbitrary weighting function w, we have ( 29 ( 29 ( 29 ( 29 0 , 0 0 0 , 0 0 0 w u w u w and w wfdx dx ku dx du u dx du a dx d w L L 2200 = 2200 = + + - If we apply the integration by parts to the first term, we have w wfdx dx wku dx du wu dx du a dx dw dx du wa w wfdx dx ku dx du u dx du a dx d w L L L x x L L 2200 = + + + - 2200 = + + - = = , , 0 0 0 0 0 If we have additional boundary condition L x at dx du a = = 0 we may have the weighted residual formulation ( 29 0 0 0 . . , 0 0 0 = = = 2200 = + + x at u u and w t s w wfdx dx wku dx du wu dx du a dx dw L L 2. Weighted Residual Method Starting from the given boundary value problem

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( 29 ( 29 ( 29 0 , 0 , , 0 , 0 = = = - = + - = + = - = L x b x b x dx du a u u and P dx du a dx du a L b b x f ku dx du a dx d we have ( 29 ( 29 ( 29 . 0 0 . . , 0 0 . . , , , 0 0 0 0 0 0 0 0 0 = 2200 + = + = 2200 =
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