Composite Quadrature Formulas, Numerical Methods #3

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Angewandte Mathematik für Ingenieure

Published on Aug 31, 2024
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How can the area under the graph of a Riemann-integrable function over a compact interval be approximated using the compound quadrature formulas? In this video, physicist Dietmar Haase derives the compound quadrature formulas for rectangles, trapezoids and parabolas, which then lead to the compound rectangle rule, compound trapezoid rule and compound Simpson rule. The initial interval under consideration is first broken down into n equidistant subintervals with n+1 support points and then one of the three elementary quadrature formulas is applied to each of these subintervals. Using a selected example, the three compound quadrature formulas are compared with each other, ultimately showing that the compound Simpson rule delivers the best result by far. Furthermore, the general formula for any compound quadrature formula is derived and the important terms weight, node and support point are defined on the basis of this. Website: https://www.ingmathe.de Youtube channel: / ingmathede Online calculator: https://www.wolframalpha.com/

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