Homework 3 – Math 104B,

Due on Saturday, April 25th, 2020

Instructor: Carlos J. Garc´ıa Cervera

1. (10 points) Prove that the composite Simpson’s rule is O(h

) when

applied to functions with sufficient derivatives.

2. (10 points) Consider a numerical integration rule of the form

(a) (5 points) What is the linear system that muist be solved in the

method of undetermined coefficients for finding A, B, C? Solve

for A, B, C.

(b) (5 points) What three integrals must be evaluated to determine

A, B, C in a Newton-Cotes formula? Solve for A, B, C.

3. (10 points) Show how the Gaussian quadrature rule

 

i. (5 points) Prove that this approach provides a quadrature

that is second order accurate.

ii. (5 points) Write a program that uses this approach to ap￾proximate (1), and verify the order of accuracy numerically.