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δ- Fraction solutions to riccati equations

  • S. Clement Cooper
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 1406)

Keywords

Riccati Equation Continue Fraction Coefficient Function Fraction Solution Riccati Differential Equation 
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References

  1. [1]
    Richard Bellman, Robert Kalaba and G. Milton Wing, Invariant Imbedding and Mathematical Physics. I. Partical Processes, J. Math. Phys, Vol.1, No.4, 1964, 280–308.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    J. S. R. Chisolm, Continued fraction solution of the general Riccati equation, Rational Approximation and Interpolation, Proc. of the UK-US Conf., Tampa, FL, 1983, Lecture Notes in Mathematics 1105 (Springer-Verlag, Berlin, 1984), 109–116.Google Scholar
  3. [3]
    K. D. Cooper, S. Clement Cooper, and William B. Jones, More on C-fraction solutions to Riccati equations, to appear.Google Scholar
  4. [4]
    S. Clement Cooper, William B. Jones, and Arne Magnus, General T-fraction solutions to Riccati differential equations, A. Cuyt(ed.), Nonlinear Numerical Methods and Rational Approximation, D. Reidel Publ. Co., 1988, 409–425.Google Scholar
  5. [5]
    S. Clement Cooper, General T-fraction solutions to Riccati differential equations, Ph.D. dissertation, Colorado State University, 1988.Google Scholar
  6. [6]
    Wyman Fair, Padé approximation to the solution of the Riccati equation, Math. of Comp. 18, 1964, 627–634.MathSciNetzbMATHGoogle Scholar
  7. [7]
    William B. Jones and W. J. Thron, Continued Fractions: Analytic Theory and Applications, Encyclopedia of Mathematics and Its Applications 11, Addison-Wesley Publ. Co., Reading, MA, 1980, (distributed now by Cambridge Univ. Press, NY).zbMATHGoogle Scholar
  8. [8]
    J. Kergomard, Continued fraction solution of the Riccati equation: Applications to acoustic horns and layered-inhomogeneous media, with equivalent electrical circuits, to appear in Wave Motion.Google Scholar
  9. [9]
    Alan J. Lamb, Algebraic aspects of generalized eigenvalue problems for solving Riccati equations, C. F. Byrnes and A. Lindquist (eds.), Computational and Combinatorial Methods in Systems Theory, Elsevier Science Publ. B. V., North Holland, 1986, 213–227.Google Scholar
  10. [10]
    L. J. Lange, δ-fraction expansions of analytic functions, Analytic Theory of Continued Fractions, Proc., Loen, Norway 1981, Lecture Notes in Mathematics 932 (Springer-Verlag, Berlin 1982), 152–175.Google Scholar
  11. [11]
    L. J. Lange, δ-fraction expansions for analytic functions, SIAM J. Math. Anal., Vol. 14, No. 2, March 1983, 323–368.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    G. C. McVittie, The mass-partical in an expanding universe, Mon. Not. Roy. Ast. Soc. 93, 1933.Google Scholar
  13. [13]
    G. C. McVittie, Elliptic functions in spherically symmetric solutions of Einstein’s equations, Ann. Inst. Henri Poincaré, Vol. 40, No. 3, 1984.Google Scholar
  14. [14]
    E. P. Merkes and W. T. Scott, Continued fraction solutions of the Riccati equation, J. Math. Anal. Appl. 4, 1962, 309–327.MathSciNetCrossRefzbMATHGoogle Scholar
  15. [15]
    A. N. Stokes, Continued fraction solutions of the Riccati equation, Bull. Austral. Math. Soc. 25, 1982, 207–214.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • S. Clement Cooper
    • 1
  1. 1.Department of Pure and Applied MathematicsWashington State UniversityPullman

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