Civil and Environmental Engineering 2219A/B Lecture Notes - Lecture 29: Richardson Extrapolation, Numerical Integration
28 Mar 2019
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Document Summary
Numerical integration of functions: efficient schemes day 2. The methods we will see today will help us to efficiently increase the accuracy. Richardson provides an accurate integral estimate by combining two less accurate integral estimates (richardson = trapz) Gauss quadrature provides superior integral estimates by picking optimal x-values at which to evaluate the function. Adaptive quadrature provides an accurate integral estimate (higher-order polynomial in a. Simpson estimate) by combining two less accurate integral estimates (adaptive = lower- order polynomial simpson estimate) Adaptive quadrature provides a means to create a more accurate integral estimate by combining two less accurate integrals. Basically, you apply composite simpson"s 1/3 rule to subintervals of the problem. This is more efficient for low accuracy or non-smooth functions. It"s a very similar procedure to the methods we looked at yesterday, just with a different formula for the steps.
