Abstract
In this paper, we develop corrected quadrature formulas by approximating the derivatives of the integrand that appear in the asymptotic error expansion of the quadrature, using only the function values in the original quadrature rule. A higher order convergence is achieved without computing additional function values of the integrand.
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Communicated by C.A. Micchelli
This author is in part supported by National Science Foundation under grant DMS-9504780 and by NASA-OAI Summer Faculty Fellowship (1995).
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Ford, W.F., Xu, Y. & Zhao, Y. Derivative corrections for quadrature formulas. Adv Comput Math 6, 139–157 (1996). https://doi.org/10.1007/BF02127701
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DOI: https://doi.org/10.1007/BF02127701