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International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

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Symbolic Romberg integration using Mathematica
by
Ali Yazici
Computer Engineering Department, Atilim University, Ankara ,Turkey
Coauthors: Tanil Ergenc(Department of Mathematics, METU), Yilmaz Akyildiz(Department of Mathematics, Boshporus University, Istanbul, Turkey)

High order approximations of an integral can be obtained by taking the linear combination of lower degree approximations in a systematic way. One of these approaches for 1-d integrals is known as Romberg Integration and is based upon the composite trapezoidal rule approximations and the well-known Euler-Maclaurin expansion of the error in the approximation. Because of its theoretical nature, students in a classical Numerical Analysis course usually find it difficult to follow. In order to overcome the difficulty, Mathematica software is utilized to illustrate the method, and the underlying theory. For this purpose, a Mathematica program and a set of experiments are designed to explain the method and it's intricacies in a stepwise manner. The program is expected to help the student to learn and apply the method to 1-d finite integrals. However, with minor modifications, it is possible to extend the method to multi-dimensional integrals.

Date received: December 28, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-26.