## Masters Theses

#### Abstract

"When integrating numerically, if the integrand can be expressed exactly as a polynomial of degree n, over a finite interval; then either Simpson's rule, Romberg integration, Legendre-Gauss or Jacobi-Gauss quadrature formulas provide good results. However, if the integrand can not be expressed exactly as an nth degree polynomial, then perhaps it can be expressed as a function f(x) divided by √1-x ^{2}, or as a function g(x) times (1-x)^{α } (l+x)^{ß }, where α and ß are some real numbers >1, or as a function h(x) times one. If this is the case then the Chebyshev-Gauss, Jacobi-Gauss, and Legendre- Gauss quadrature are respectively quite useful. If the integrand can not be expressed as f(x)/ √1-x ^{2} or as g(x)·(1-x) ^{α }·(1+x) ^{ß } or as h(x) ·(1) then the Romberg method should be used.

If the interval of integration is [0,∞] or [-∞,∞], then the Laguerre-Gauss and the Hermite-Gauss methods respectively are generally quite useful.

The results of this study indicate that the quadrature formula to use in a given situation is dependent upon the interval of integration and the integrand. However, the results also indicate certain guide lines for choosing the type of quadrature formula to use in a given situation"--Abstract, page iii.

#### Advisor(s)

Gillett, Billy E.

#### Committee Member(s)

Lee, Ralph E., 1921-2010

Carlile, Robert E.

Mayhan, Kenneth G.

#### Department(s)

Computer Science

#### Degree Name

M.S. in Computer Science

#### Publisher

University of Missouri at Rolla

#### Publication Date

1966

#### Pagination

iv, 120 pages

#### Note about bibliography

Includes bibliographical references (pages 118-119).

#### Rights

© 1966 Edward Lee Sartore, All rights reserved.

#### Document Type

Thesis - Open Access

#### File Type

text

#### Language

English

#### Library of Congress Subject Headings

Numerical integration

Numerical analysis -- Data processing

Gaussian quadrature formulas

#### Thesis Number

T 1955

#### Print OCLC #

5977990

#### Electronic OCLC #

910315757

#### Link to Catalog Record

http://laurel.lso.missouri.edu/record=b1068358~S5#### Recommended Citation

Sartore, Edward Lee, "Comparative analysis of numerical integration techniques" (1966). *Masters Theses*. 2953.

http://scholarsmine.mst.edu/masters_theses/2953