Error estimation for the composite Simpson formula, Numerical Methods #6

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Angewandte Mathematik für Ingenieure

Published on Sep 21, 2024
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How can the absolute approximation error be estimated upwards when calculating a definite integral using the compound Simpson formula? In this video, physicist Dietmar Haase shows how the absolute approximation error can be estimated upwards when calculating a definite integral using the compound Simpson formula. First, the definite integral to be calculated is approximated using only a single parabola and then this result is used to approximate the initial interval broken down into 2n equidistant subintervals. It turns out that if the interval width of the subintervals is halved, the absolute error is reduced to 1/16. In principle, the value of a definite integral can be approximated with any degree of accuracy using the compound Simpson formula by suitably reducing the subinterval width. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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