Methods for evaluating a definite integral within a specified error are examined. The Clenshaw-Curtis formula is considered to be the most useful and estimates to the error in this formula are given. Checks on the reliability of these error estimates are also given. There liability of quadrature error estimates in general is discussed along with the means for reducing the probability of failure of these error estimates. Algorithms for the evaluation of integrals by interval subdivision are discussed. The practical application of these integration methods is examined in the evaluation of collision integrals from which the transport properties of gases can be derived. Finally, a usefulway of generating a large number of integrals is outlined.
| Date of Award | 1969 |
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| Original language | English |
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| Awarding Institution | - Queen's University Belfast
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The automatic evaluation of definite integrals
O'Hara, H. J. (Author). 1969
Student thesis: Doctoral Thesis › Doctor of Philosophy