Numerical Integration

More documents

Recommendations

Info

Simpson’s 1/3 Rule: Example • <strong>Numerical</strong>ly integrate: f ( x ) = 0.2 + 25x − 200x + 675x 2 3 − 900x 4 + 400x 5 x 0 = 0, x 2 = 0.8, n = 4 (Analytical answer = 1.6405333) © 2003-2006 Roberto Muscedere 26
I f Simpson’s 1/3 Rule: Example (0.4) ≅ f ( 0) = 0.2 f (0.2) = 1.288 = 2.456 f (0.6) = 3.464 f (0.8) 0.232 ⎛ 0.2 + 4(1.288 + 3.464) + 2(2.456) + 0.232 ⎞ 0.8⎜ ⎟ ⎝ 12 ⎠ =1.62346667 • Better than with Trapezoidal Rule with eight segments (1.6008) = © 2003-2006 Roberto Muscedere 27
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 and 24: Simpson’s 1/3 Rule • Add a seri
Page 25: Simpson’s 1/3 Rule • Grouping t
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

Create successful ePaper yourself

Delete template?

Save as template?