Romberg integration: a symbolic approach with mathematica

  • Authors:

  • Ali Yazici;Tanil Ergenç;Irfan Altas

  • Affiliations:

  • Computer Engineering Department, Atilim University, Ankara, Turkey;Mathematics Department, Middle East Technical University, Ankara, Turkey;School of Information Studies, Wagga Wagga, Australia

  • Venue:
  • ICCS'03 Proceedings of the 1st international conference on Computational science: PartI
  • Year:
  • 2003

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Abstract

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.