Romberg integration: A symbolic approach with mathematica

Yazici A., Ergenc T., Altas I.

COMPUTATIONAL SCIENCE - ICCS 2003, PT I, PROCEEDINGS, vol.2657, pp.691-700, 2003 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 2657
  • Publication Date: 2003
  • Journal Name: COMPUTATIONAL SCIENCE - ICCS 2003, PT I, PROCEEDINGS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, EMBASE, MathSciNet, Philosopher's Index, zbMATH
  • Page Numbers: pp.691-700
  • Middle East Technical University Affiliated: No

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.