Register to reply

Trapezoidal, simpsons rule, and higher order approximations

Share this thread:
okkvlt
#1
Dec4-09, 09:25 AM
P: 53
hi. i was able to prove the trapezoidal rule and simpsons rule. (basically i used matrices to determine the coefficients m and b for mx+b when proving the trapezoidal rule and a,b,c for ax^2+bx+c such that the points coincide, then i integrated the approximating polynomial) the amount of number-crunching and expanding products of linear terms was probably the most work ive ever done, but i was amazed to see terms cancel out to yeild vastly simplified formulas. but i was wondering, suppose i approximated each step with suppose, a cubic equation. i know how to do this, but after setting up the 4x4 matrix i quickly realized that this would be extremely mundane due to all the algebraic manipulations. so before i try deriving a numerical method that uses cubics to approximate the curve pieces, i wanna know whether it will simplify. will it simplify?
Phys.Org News Partner Science news on Phys.org
Flapping baby birds give clues to origin of flight
Prions can trigger 'stuck' wine fermentations, researchers find
Socially-assistive robots help kids with autism learn by providing personalized prompts
arildno
#2
Dec4-09, 09:36 AM
Sci Advisor
HW Helper
PF Gold
P: 12,016
You can look upon Newton-Cotes formulae, and Gaussian quadrature to see how these numerical techniques have been developed:
http://mathworld.wolfram.com/Newton-CotesFormulas.html


Register to reply

Related Discussions
Quotient rule for higher order derivatives Calculus 17
Higher order partial derivatives and the chain rule Calculus & Beyond Homework 5
Bayes rule using higher order prior probability Set Theory, Logic, Probability, Statistics 1
Trapezoidal Rule Calculus 11