Example of error estimation for the composite trapezoidal formula, Numerical Methods #5

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Angewandte Mathematik für Ingenieure

Published on Sep 14, 2024
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How can the number of support points or the number of equidistant subintervals required to calculate a definite integral using the compound trapezoidal formula for a given absolute error? In this video, physicist Dietmar Haase uses the Gaussian bell curve, which is relevant in probability theory, to show how the absolute error for calculating the definite integral can be estimated upwards using the compound trapezoidal formula. Because the antiderivative of the Gaussian bell curve does exist but cannot be represented analytically using elementary functions, explicit evaluation relies on numerical approximation methods. In particular, it shows how the minimum number of support points or the minimum number of equidistant subintervals required can be determined for a given absolute error so that the required absolute error can be met with certainty.

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