mtl_gen_int_ppt_romberg

# mtl_gen_int_ppt_romberg - Romberg Rule of Integration...

This preview shows pages 1–8. Sign up to view the full content.

1/10/2010 http://numericalmethods.eng.usf.edu 1 Romberg Rule of Integration Major: All Engineering Majors Authors: Autar Kaw, Charlie Barker http://numericalmethods.eng.usf.edu Transforming Numerical Methods Education for STEM Undergraduates

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Romberg Rule of Integration http://numericalmethods.eng.usf.edu
http://numericalmethods.eng.usf.edu 3 Basis of Romberg Rule Integration = b a dx ) x ( f I The process of measuring the area under a curve. Where: f(x) is the integrand a= lower limit of integration b= upper limit of integration f(x) a b y x b a dx ) x ( f

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
http://numericalmethods.eng.usf.edu 4 What is The Romberg Rule? Romberg Integration is an extrapolation formula of the Trapezoidal Rule for integration. It provides a better approximation of the integral by reducing the True Error.
http://numericalmethods.eng.usf.edu 5 Error in Multiple Segment Trapezoidal Rule The true error in a multiple segment Trapezoidal Rule with n segments for an integral Is given by = b a dx ) x ( f I ( ) ( ) n f n a b E n i i t = ξ = 1 2 3 12 where for each i, is a point somewhere in the domain , . i ξ ( ) [ ] ih a , h i a + + 1

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
http://numericalmethods.eng.usf.edu 6 Error in Multiple Segment Trapezoidal Rule The term can be viewed as an ( ) n f n i i = ξ 1 approximate average value of in . ( ) x f [ ] b , a This leads us to say that the true error, E t previously defined can be approximated as 2 1 n E t α
7 Error in Multiple Segment Trapezoidal Rule Table 1 shows the results obtained for the integral using multiple segment Trapezoidal rule for n Value E t 1 11868 807 7.296 --- 2 11266 205 1.854 5.343 3 11153 91.4 0.8265 1.019 4 11113 51.5 0.4655 0.3594 5 11094 33.0 0.2981 0.1669 6 11084 22.9 0.2070 0.09082 7 11078 16.8 0.1521 0.05482 8 11074 12.9 0.1165 0.03560 = 30 8 8 9 2100 140000 140000 2000 dt t . t

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This note was uploaded on 06/12/2011 for the course EML 3041 taught by Professor Kaw,a during the Spring '08 term at University of South Florida - Tampa.

### Page1 / 27

mtl_gen_int_ppt_romberg - Romberg Rule of Integration...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online