Alternative to the Romberg Method of Estimating the Definite Integral

Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This approximation and its composite, in their general forms, are shown to ha...

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Bibliographic Details
Published inarXiv.org
Main Author Michael Brandon Youngberg
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 03.08.2012
Subjects
Approximation
Error reduction
Extrapolation
Mathematical analysis
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Summary:Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This approximation and its composite, in their general forms, are shown to have predictable error patterns; thus, an extrapolation method can be used to increase the accuracy. We then derive the necessary weights to use an extrapolation method to reduce error and converge more quickly than Romberg integration by allowing for improved accuracy with fewer necessary subintervals. The procedure necessary to implement this alternative method is then carefully described, followed by two examples.
ISSN:2331-8422