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Unformatted text preview: continuous second derivatives at all interior nodes ( x i , y i ); i = 2 : n − 1 , are given by f i ( x ) = 1 6 h i £ ( x i +1 − x ) 3 f 00 i + ( x − x i ) 3 f 00 i +1 ¤ + · y i h i − h i 6 f 00 i ¸ ( x i +1 − x ) + · y i +1 h i − h i 6 f 00 i +1 ¸ ( x − x i ) x i ≤ x ≤ x i +1 ; i = 1 : n − 1 Assume that the second derivatives f 00 i ; i = 1 : n are known for a particular type of spline at all interior nodes. Draw a F owchart which evaluates the above splines at m locations z j ; j = 1 : m. 4. (30 pts.) Simpson’s quadrature is given by x 2 Z x f ( x ) dx ≈ h 3 ( f + 4 f 1 + f 2 ) (a) Determine the degree of precision for that quadrature. (b) Derive the corresponding composite quadrature in order to integrate f ( x ) over the range [ a, b ] . (c) Draw a F owchart which implements the results of Part (b) in MATLAB. 1...
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This note was uploaded on 07/20/2009 for the course AME 404 taught by Professor Dravinski during the Fall '05 term at USC.
 Fall '05
 Dravinski

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