An efficient algorithm for calculating taylor polynomials of implicit functions

John T. White, Edward Allen, Keshab Ganguly, Lawrence Schovanec

Research output: Contribution to journalArticlepeer-review

Abstract

An iterative procedure is introduced which generates the Taylor expansion of an implicitly defined function f(x)∊R,x∊Rn, that satisfies an equation F(x,f(x)) = 0. In particular the mth iterate is precisely the mth degree Taylor polynomial of f(x). The algorithm is implemented by using a symbolic manipulation language. Examples are presented which illustrate the pertinent features of the method and the procedure is employed to solve some transcendental equations that arise in neutron transport calculations.

Original languageEnglish
Pages (from-to)137-145
Number of pages9
JournalInternational Journal of Computer Mathematics
Volume31
Issue number3-4
DOIs
StatePublished - Jan 1 1990

Keywords

  • Implicit function
  • Taylor polynomials
  • contractive map
  • fixed point
  • neutron transport
  • symbolic processor

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