70 3 h I f f f f f e e e e 10 September 2014 ME262 Numerical Analysis Sessional

70 3 h i f f f f f e e e e 10 september 2014 me262

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10 September 2014 ME262 Numerical Analysis Sessional 12 12 Approximate the function by a cubic polynomial Simpson’s 3/8 -Rule 0 1 2 3 3 ( ) ( ) 3 ( ) 3 ( ) ( ) 8 b a h f x dx f x f x f x f x 1 3 m k 3k-3 3k-2 3k-1 3k 3h I = f x + 3f x f x f x 8 x 0 x 1 x f(x) x 2 h h L(x) x 3 h n must be a multiple of 3 3 n m
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10 September 2014 ME262 Numerical Analysis Sessional 13 Example: Simpson’s Rules Evaluate the integral Simpson’s 1/3 -Rule Simpson’s 3/8 -Rule dx xe 4 0 x 2 % . . . . . ) ( ) ( ) ( ) ( 96 57 926 5216 411 8240 926 5216 411 8240 e 4 e 2 4 0 3 2 4 f 2 f 4 0 f 3 h dx xe I 8 4 4 0 x 2 % 71 . 30 926 . 5216 209 . 6819 926 . 5216 209 . 6819 832 . 11923 ) 33933 . 552 ( 3 ) 18922 . 19 ( 3 0 8 ) 4/3 ( 3 ) 4 ( f ) 3 8 ( f 3 ) 3 4 ( f 3 ) 0 ( f 8 h 3 dx xe I 4 0 x 2
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10 September 2014 ME262 Numerical Analysis Sessional 14 Combined Simpson’s 1/3 & 3/8 Rule 1/ 3 3/ 8 1/ 3 3/ 8 2 1 3 1 3 3 p q p p j q q k
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