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Romberg Integration: A Symbolic Approach with Mathematica

BROWSE_DETAIL_CREATION_DATE: 17-09-2015

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BROWSE_DETAIL_TYPE: Article

BROWSE_DETAIL_PUBLISH_STATE: Published

BROWSE_DETAIL_FORMAT: No File

BROWSE_DETAIL_LANG: English

BROWSE_DETAIL_SUBJECTS: SCIENCE, Mathematics,

BROWSE_DETAIL_CREATORS: Yazıcı, Ali (Author), Ergenç, Tanıl (Author), Altas, İrfan (Author),

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Higher order approximations of an integral can be obtained from lower order ones in a systematic way. For 1-D integrals Romberg Integration is an example which is based upon the composite trapezoidal rule and the well-known Euler-Maclaurin expansion of the error. In this work, Mathematica is utilized to illustrate the method and the underlying theory in a symbolic fashion. This approach seems plausible for discussing integration in a numerical computing laboratory environment.


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    Springer International Publishing AG


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    BROWSE_DETAIL_TAB_REFERENCES1.Joyce, D.C.: Survey of Extrapolation Processes in Numerical Analysis, SIAM Review, 13,4 (1971) 435–490.MATHCrossRefMathSciNet2.Romberg. W.: Vereinfachte Numerische Integration, Kgl. Nordske Vid. Selsk. Forh, bf 28 (1955) 30–36.MATHMathSciNet3.Yazıcı, A.: On the Subdivision Sequences of Extrapolation Method of Quadrature, METU Journal of Pure and Applied Sciences, 23,1 (1990) 35–51.4.Burden, R.L. and Faires, J.D.: Numerical Analysis, 3rd. Ed., PWS Publishers (1985).5.Kelch, R.: Numerical Quadrature by Extrapolation with Automatic Result Verification, in Scientific Computing with Automatic result Verification, Academic Press, Inc. (1993) 143–185.6.Lyness, J.N. and Mc Hugh, B.J.J.: On the Remainder Term in the N-Dimensional Euler-Maclaurin Expansion, Num.Math., 15 (1970) 333–344.MATHCrossRefMathSciNet7.Skeel, R.D. and Keiper, J.B.: Elementary Numerical Computing with Mathematica, McGraw-Hill (1993).8.Mathews, J.H. and Fink, K.D.: Numerical Methods Using Matlab, 3rd Edition, Prentice Hall (1999).9.Wolfram, S.: The Mathematica Book, Cambridge University Press (1999).10.Johnston, R.L.: Numerical Methods: A Software Approach, John Wiley and Sons (1982).


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