Exit criteria for Simpson’s compound rule

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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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