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Continued fraction solution of the general Riccati equation

  • Approximation And Interpolation Theory
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Rational Approximation and Interpolation

Part of the book series: Lecture Notes in Mathematics ((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.

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References

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Authors and Affiliations

  1. Mathematical Institute, University of Kent, Canterbury, Kent, England

    J. S. R. Chisholm

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  1. J. S. R. Chisholm
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Peter Russell Graves-Morris Edward B. Saff Richard S. Varga

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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

  • eBook Packages: Springer Book Archive

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