Abstract
We construct a general T-fraction solution to a Riccati differential equation. The general T-fraction corresponds to a formal power series solution of the Riccati equation at z = 0 and to a formal Laurent series solution at z = ∞. If the T-fraction converges uniformly in a neighborhood of z = 0, then it converges to the unique analytic solution of the Riccati equation that vanishes at z = 0. A similar result holds at z = ∞. Finally an example is given.
Research supported in part by the National Science Foundation under Grant No. DMS-84–01717
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© 1988 D. Reidel Publishing Company
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Cooper, S.C., Magnus, A., Jones, W.B. (1988). General T—Fraction Solutions to Riccati Differential Equations. In: Cuyt, A. (eds) Nonlinear Numerical Methods and Rational Approximation. Mathematics and Its Applications, vol 43. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2901-2_22
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DOI: https://doi.org/10.1007/978-94-009-2901-2_22
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-7807-8
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