An optimal exponential method for improved calculation of laplace integrals and power series

Owen T. Hanna, Richard A. Davis

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

A new general procedure developed here improves the calculation of both Laplace-type integrals and convergent power series: ∫0 tαexp(-xt)F(t)dt and ∑n=1 anxn Integrals and series of this type (which often depend on parameters) arise frequently in the solution of important chemical engineering problems, especially in the transport and chemical reaction areas. The results of this study yield convenient analytical approximations. A recursive algorithm determines the required numerical coefficients with the aid of a computer. Several examples illustrate the features of the new technique. Some comparisons are made to earlier improvement methods, such as Padé approximation.

Original languageEnglish (US)
Pages (from-to)1603-1629
Number of pages27
JournalChemical Engineering Communications
Volume198
Issue number12
DOIs
StatePublished - Dec 1 2011

Keywords

  • Asymptotics
  • Differential equations
  • Integrals
  • Power series
  • Regular perturbations
  • Watson's lemma

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