Exit criteria for Simpson's compound rule

Authors:
J. H. Rowland and Y. L. Varol

Journal:
Math. Comp. **26** (1972), 699-703

MSC:
Primary 65D30

MathSciNet review:
0341823

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Abstract: In many automated numerical algorithms, the calculations are stopped when the difference between two successive approximations is less than a preassigned tolerance. The dependability of this procedure for Simpson's compound rule has been investigated. Classes of functions have been determined for which the above criterion is (a) always valid, and (b) asymptotically valid. A new exit rule is proposed which appears to be less conservative than the standard technique.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0341823-8

Keywords:
Numerical integration,
exit criteria,
stopping inequality

Article copyright:
© Copyright 1972
American Mathematical Society