Numerical Integration

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Simpson’s 1/3 Rule • Substituting Simpson’s 1/3 rule for each integral yields: I ≅ + f ( x ) + 4 f ( x ) + f ( x 0 1 2 h 2 f ( x ) + 4 f ( x ) + f ( x ) 2h 2 3 4 6 f ( x ) + 4 f ( x + L + 2hh n− n− 6 6 ) ) + ( x 2 1 n f ) © 2003-2006 Roberto Muscedere 24
Simpson’s 1/3 Rule • Grouping the terms: I ≅ ⎛ ⎜ ⎝ x − x ⎞ ⎟ ⎠ ⎡ ⎢ ⎢ f n−1 ∑ ( x ) + 4 f ( x ) 0 i n 0 ⎢ i = 1,3,5 3n ⎢ n − 2 ⎢ + 2 ∑ f ( x ) j= 2,4, 6 ⎢ ⎣ + f ( x j n ⎤ ⎥ ⎥ ⎥ ) ⎥ ⎦ • n must be even © 2003-2006 Roberto Muscedere 25
Page 1 and 2: Numerical Integration • Newton-Co
Page 3 and 4: Trapezoidal Rule • Trapezoidal Ru
Page 5 and 6: Trapezoidal Rule • Same result if
Page 7 and 8: Trapezoidal Rule: Example f (0) = 0
Page 9 and 10: Trapezoidal Rule • Add a series o
Page 11 and 12: • Grouping the terms: Trapezoidal
Page 13 and 14: Trapezoidal Rule: Example f (0) = 0
Page 15 and 16: Trapezoidal Code (p.2) double Integ
Page 17 and 18: Trapezoidal Code -Output n=1, I=0.1
Page 19 and 20: Simpson’s 1/3 Rule ( x − x1 )(
Page 21 and 22: Simpson’s 1/3 Rule: Example • N
Page 23: Simpson’s 1/3 Rule • Add a seri
Page 27 and 28: I f Simpson’s 1/3 Rule: Example (
Page 29 and 30: Simpson’s 1/3 Code (p.2) double I
Page 31 and 32: Simpson’s 1/3 Code (p.4) double F

Numerical Integration

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