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Math 481a, Spring 2005 Project 3. Richardson Extrapolation

Summary: Math 481a, Spring 2005
Project 3. Richardson Extrapolation
Due December 9, 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 101, 201, 1001, and 2001 equally spaced nodes (this corresponds to the
step sizes h = 0.0099, h/2, h/10, and h/20). Observe, that the error of
approximation decreases in complete agreement with the formula in Theo-
rem 4.5 on page 200. In particular, that the error drops down 100 times for
h/10 as expected.
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,


Source: Alekseenko, Alexander - Department of Mathematics, California State University, Northridge


Collections: Physics