Summary: Math 481a, Spring 2005
Project 3. Richardson Extrapolation
Due May 18, 2005
Problem 1: Analysis of performance of the Richardson extrapolation.
· Write a function implementing the Composite Trapezoidal Rule for calcu-
lating the integral
1-x2 dx. Keep your programming so that you can
change the number of nodes easily.
· Calculate approximations of the integral by the Composite Trapezoidal rule
with 100, 200, 1000, and 2000 equally spaced nodes (this corresponds to the
step sizes h = 0.01, h/2, h/10, and h/20). Observe, that the error of approx-
imation decreases in complete agreement with the formula in Theorem 4.5
on page 200. In particular, that the error drops down 100 times for h/10 as
· Approximate the integral by the third order Richardson approximation.
Namely, start from an assumption that the Composite Trapezoidal Rule
S(h) satisfies the following error expansion,