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2009501436_&igrave;œ&nbsp;&ecirc;&acute;‘&igrave;„&nbsp;_hw#6

# 2009501436_ìœ ê´‘ì„ _hw#6

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Home Work. #6 Problem Set 3.1 3.1.11) where is the largest error? Sol) (1) exact solution : 2 3 1 1 " ' 2 6 u x u x A u x Ax B - = = - + = - + + (0) (1) 0 u u = = 1 , 0 6 A B = = 3 1 1 6 6 u x x = - + (2) approximation : 1 1 0 0 ( ) ( ) ( ) ( ) ( ( ) ( )) i i i i i F f x V x dx f x x dx V x x φ φ = = = 1 1 1 1 1 0 1 2 2 2 2 0 1 1 2 ( ) ( ) , ( ( ) 3 (0 ), ( ) 3 2( )) 3 3 3 1 2 2 ( ) ( ) , ( ( ) 3 1 ( ), ( ) 3 3( 1)) 3 3 3 F f x x dx x x x x x x F f x x dx x x x x x x φ φ φ φ φ φ = = < < = - + < < = = - < < = - + < < 1 2 1 2 , 9 9 F F = = 1 0 1 1/3 2/3 1 1 11 0 0 1/3 2/3 12 1/3 2/3 1 22 1/3 2/3 ( ) ( ) ( ) , ( ( ) 1) ( ) ( ) (3)(3) ( 3)( 3) 6 ( 3)( 3) 3 (3)(3) ( 3)( 3) 6 j i ij d x dV x K c x dx c x dx dx d x d x K dx dx dx dx dx K dx K dx dx φ φ φ = = = = + - - = = - - = - = + - - = 1 1 2 2 6 3 1/9 0.0494, 0.0617 3 6 2/9 u KU F u u u - = = = = = - Largest error : 0.0116 at x =0.84 2009-05-13

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Home Work. #6 3.2.17) Plot ( ) f x and the two interpolating splines for 0 1 x ==> Green : n=20, + , Blue : n=10, o Interval : 0 1 x Green : n=20, + , Blue : n=10, o Interval : 0 0.2 x 2009-05-13
Home Work. #6 Problem Set 3.3 3.3.8) If 2 u x = in the square { 1 , 1} S x y = - ≤ , compute both sides when.

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