Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

A STUDY ON THE ERROR BOUNDS OF TRAPEZOIDAL AND SIMPSON@S QUADRATURES

  • CHOI SUNG HEE (Division of Computer and Information Sciences, Sun Moon University) ;
  • HWANG SUK HYUNG (Division of Computer and Information Sciences, Sun Moon University) ;
  • HONG BUM IL (Department of Mathematics and Institute of Natural Sciences, Kyunghee University)
  • 발행 : 2005.01.01

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초록

In this paper, we discuss the average case errors of some numerical quadratures, namely Trapezoidal and Simpson's, in the numerical integration problem. Our integrands are r-fold Wiener functions from the interval [0,1] and only at finite number of points the function values are evaluated. We study average case errors of these quadratures theoretically and then compare it with our practical (a posteriori) researches. Monte-Carlo simulation is used to perform these empirical researches. Finally we empirically compute the error bounds of studied quadratures for the higher degrees of Wiener functions.

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