Numerical Integration
Numerical Integration Numerical Integration
Trapezoidal Rule: Example • Why so bad? © 2003-2006 Roberto Muscedere 8
Trapezoidal Rule • Add a series of intervals b − a = x = a x = b n n h 0 x 1 x 2 x n I = ∫ f + + + ( x ) dx ∫ f ( x ) dx L ∫ f ( x ) dx x 0 x 1 x n− 1 © 2003-2006 Roberto Muscedere 9
- 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: Trapezoidal Rule: Example f (0) = 0
- 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 and 26: Simpson’s 1/3 Rule • Grouping t
- 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
Trapezoidal Rule<br />
• Add a series of intervals<br />
b − a<br />
= x = a x = b<br />
n<br />
n<br />
h<br />
0<br />
x<br />
1<br />
x<br />
2<br />
x n<br />
I<br />
=<br />
∫<br />
f + + +<br />
( x<br />
) dx<br />
∫<br />
f<br />
( x<br />
) dx L ∫<br />
f<br />
( x<br />
) dx<br />
x<br />
0<br />
x<br />
1<br />
x n− 1<br />
© 2003-2006 Roberto Muscedere 9
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