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

Owen T. Hanna, Richard A. Davis

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Chemical engineering
Chemical reactions

Keywords

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

Cite this

An optimal exponential method for improved calculation of laplace integrals and power series. / Hanna, Owen T.; Davis, Richard A.

In: Chemical Engineering Communications, Vol. 198, No. 12, 01.12.2011, p. 1603-1629.

Research output: Contribution to journalArticle

@article{826bbfd365ef4e47a00461e2a30472b4,
title = "An optimal exponential method for improved calculation of laplace integrals and power series",
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 Pad{\'e} approximation.",
keywords = "Asymptotics, Differential equations, Integrals, Power series, Regular perturbations, Watson's lemma",
author = "Hanna, {Owen T.} and Davis, {Richard A.}",
year = "2011",
month = "12",
day = "1",
doi = "10.1080/00986445.2011.565525",
language = "English (US)",
volume = "198",
pages = "1603--1629",
journal = "Chemical Engineering Communications",
issn = "0098-6445",
publisher = "Taylor and Francis Ltd.",
number = "12",

}

TY - JOUR

T1 - An optimal exponential method for improved calculation of laplace integrals and power series

AU - Hanna, Owen T.

AU - Davis, Richard A.

PY - 2011/12/1

Y1 - 2011/12/1

N2 - 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.

AB - 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.

KW - Asymptotics

KW - Differential equations

KW - Integrals

KW - Power series

KW - Regular perturbations

KW - Watson's lemma

UR - http://www.scopus.com/inward/record.url?scp=80051916755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80051916755&partnerID=8YFLogxK

U2 - 10.1080/00986445.2011.565525

DO - 10.1080/00986445.2011.565525

M3 - Article

VL - 198

SP - 1603

EP - 1629

JO - Chemical Engineering Communications

JF - Chemical Engineering Communications

SN - 0098-6445

IS - 12

ER -