MATH3242.03/COSC3122.03

FW03

Assignment 3 Due: Fri., Feb. 27, 2004

1. Use adaptive integration methods with the composite Simpson's Rule to evaluate

correct to 4 decimal places.

2. Put the following integrals into standard form for

(a) Gauss-Legendre integration:

(b) Gauss-Laguerre integration:

(c) Gauss-Chebyshev integration: (Hint: make the substitution x = cosu).

3. For what values of p do the following integrals converge:

4. For what values of q do the following integrals converge:

5. Evaluate the integral

by treating the singular part analytically and integrating the remainder using the elementary Simpson's Rule.

6 Write a computer program to perform Gauss-Legendre integration with n points for an integral in standard form. Use the IMSL FORTRAN program DGQRUL or the C program gauss_quad_rule to generate the required roots and weights for both n = 5 and n = 10. Use this program to evaluate both the integrals in question 2(a) using both 5 and 10 points.

7 Write a computer program to perform Gauss-Laguerre integration with n points for an integral in standard form. Use the IMSL programs referred to in question 6 to generate the required roots and weights for n = 10. Use this program to evaluate the integral in question 2(b).

8. (a) Use the IMSL FORTRAN routine DQDAG or the C program int_fcn for adaptive integration to evaluate the integral

Output the error estimate provided by the routine as well as the value for the integral itself.

(b) Use the IMSL FORTRAN routine DQDAGI or the C program int_fcn_inf to evaluate the integral

Output the error estimate provided by the routine as well as the value for the integral itself.