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Continued fraction solution of the general Riccati equation

Approximation And Interpolation Theory

Part of the Lecture Notes in Mathematics book series (LNM,volume 1105)

Abstract

The general Riccati equation is reduced to the standard form z′(x)=b0(x) − z2(x). Successive iterations of a continued fraction solution of this equation are given in terms of a sequence {br(x); r=1,2,…} of functions which replace b0(x) in the standard form, and which are defined in terms of b0(x) and its derivatives.

Keywords

  • Riccati Equation
  • Perturbation Series
  • Riccati Differential Equation
  • Pade Approximants
  • Pade Approximation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© 1984 Springer-Verlag

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Chisholm, J.S.R. (1984). Continued fraction solution of the general Riccati equation. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072403

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  • DOI: https://doi.org/10.1007/BFb0072403

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13899-0

  • Online ISBN: 978-3-540-39113-5

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