CSC_349_HANDOUT#28

CSC_349_HANDOUT#28 - COMPUTER SCIENCE 349A Handout Number...

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1 COMPUTER SCIENCE 349A Handout Number 28 COMPOSITE (Multiple-Application) SIMPSON'S RULE (Section 21.2.2) Each application of Simpson's rule requires 2 subintervals on the interval of integration and 3 quadrature points, say x 2 j 2 , x 2 j 1 and x 2 j : o o o f(x) x x 2j-2 x 2j-1 x 2j hh [] ) ( ) ( 4 ) ( 3 ) ( 2 1 2 2 2 2 2 2 j j j x x x f x f x f h dx x f j j + + Thus, m applications of Simpson's rule on [ a , b ] require that [ a , b ] be subdivided into an even number of subintervals. In the following, we will assume that [ a , b ] is subdivided into 2 m subintervals, each of length h = b a 2 m , and the corresponding 2 m + 1 quadrature points will be denoted by m x x x x 2 2 1 0 , , , , L . The case m = 1: just one application of Simpson's rule (or, we could call this the "noncomposite" Simpson's rule). The case m = 2: two applications of Simpson's rule require 5 quadrature points and 4 subintervals of [ a , b ] , each of length h = b a 4 .
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2 o o o f(x) x xxx o o xx 01 23 4 hh = a = b Letting ) ( denote i i x f f , this approximation becomes [] . 4 2 4 3 4 3 4 3
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CSC_349_HANDOUT#28 - COMPUTER SCIENCE 349A Handout Number...

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