stability problems

… ►In practice, however, problems of severe instability often arise and in §§3.6(ii)–3.6(vii) we show how these difficulties may be overcome. … ► … ► … ►Thus in the inhomogeneous case it may sometimes be necessary to recur backwards to achieve stability. … ►For a difference equation of order

k

(

\geq 3

), …

6: 3.10 Continued Fractions

… ► … ►In contrast to the preceding algorithms in this subsection no scaling problems arise and no a priori information is needed. … ►This forward algorithm achieves efficiency and stability in the computation of the convergents

C_{n}=A_{n}/B_{n}

, and is related to the forward series recurrence algorithm. Again, no scaling problems arise and no a priori information is needed. …

7: Bibliography H

… ►

E. Hairer, S. P. Nørsett, and G. Wanner (1993) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 8, Springer-Verlag, Berlin.

ⓘ

Notes:: A reprinting with corrections appeared in 2000.
External Links:: ISBN 3-540-56670-8, MathReview, ZentralBlatt
Referenced by:: §3.7(v), §3.7(i).
Encodings:: BibTeX

►

E. Hairer, S. P. Nørsett, and G. Wanner (2000) Solving Ordinary Differential Equations. I. Nonstiff Problems. 2nd edition, Springer-Verlag, Berlin.

ⓘ

External Links:: ISBN 3-540-56670-8, Document, MathReview
Referenced by:: §32.17.
Encodings:: BibTeX

►

E. Hairer and G. Wanner (1996) Solving Ordinary Differential Equations. II. Stiff and Differential-Algebraic Problems. 2nd edition, Springer Series in Computational Mathematics, Vol. 14, Springer-Verlag, Berlin.

ⓘ

External Links:: ISBN 3-540-60452-9, MathReview, ZentralBlatt
Referenced by:: §3.7(v).
Encodings:: BibTeX

… ►

G. H. Hardy and J. E. Littlewood (1925) Some problems of “Partitio Numerorum” (VI): Further researches in Waring’s Problem. Math. Z. 23, pp. 1–37.

ⓘ

Notes:: Reprinted in Collected Papers of G. H. Hardy (Including Joint papers with J. E. Littlewood and others), Vol. I, pp. 469–505, Clarendon Press, Oxford, 1966.
External Links:: ISSN 0025-5874, Document, MathReview Entry, ZentralBlatt
Referenced by:: §27.13(iii).
Encodings:: BibTeX

… ►

H. Hochstadt (1963) Estimates of the stability intervals for Hill’s equation. Proc. Amer. Math. Soc. 14 (6), pp. 930–932.

ⓘ

External Links:: FullText, MathReview (P. Ungar), ZentralBlatt
Referenced by:: §28.29(iii).
Encodings:: BibTeX

…

8: Bibliography J

… ►

W. B. Jones and W. J. Thron (1974) Numerical stability in evaluating continued fractions. Math. Comp. 28 (127), pp. 795–810.

ⓘ

External Links:: FullText, MathReview (N. N. Abdelmalek), ZentralBlatt
Referenced by:: §3.10(iii).
Encodings:: BibTeX

… ►

N. Joshi and A. V. Kitaev (2005) The Dirichlet boundary value problem for real solutions of the first Painlevé equation on segments in non-positive semi-axis. J. Reine Angew. Math. 583, pp. 29–86.

ⓘ

External Links:: ISSN 0075-4102, Document, MathReview (Mehmet Can), ZentralBlatt
Referenced by:: §32.11(i).
Encodings:: BibTeX

►

N. Joshi and M. D. Kruskal (1992) The Painlevé connection problem: An asymptotic approach. I. Stud. Appl. Math. 86 (4), pp. 315–376.

ⓘ

External Links:: ISSN 0022-2526, MathReview (I. P. Martynov), ZentralBlatt
Referenced by:: §32.11(i), §32.12(ii).
Encodings:: BibTeX

…

9: Bibliography D

… ►

D. Dai, M. E. H. Ismail, and X. Wang (2014) Plancherel-Rotach asymptotic expansion for some polynomials from indeterminate moment problems. Constr. Approx. 40 (1), pp. 61–104.

ⓘ

External Links:: ISSN 0176-4276, Document, Link, MathReview (Francisco Marcellán), ZentralBlatt
Referenced by:: §2.9(iii), §2.9(iii).
Encodings:: BibTeX

… ►

K. Dekker and J. G. Verwer (1984) Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. CWI Monographs, Vol. 2, North-Holland Publishing Co., Amsterdam.

ⓘ

External Links:: ISBN 0-444-87634-0, MathReview (A. de Castro Brzezicki), ZentralBlatt
Referenced by:: §3.7(v).
Encodings:: BibTeX

… ►

R. C. Desai and M. Nelkin (1966) Atomic motions in a rigid sphere gas as a problem in neutron transport. Nucl. Sci. Eng. 24 (2), pp. 142–152.

ⓘ

Referenced by:: §18.39(iii).
Encodings:: BibTeX

… ►

P. G. Drazin and W. H. Reid (1981) Hydrodynamic Stability. Cambridge University Press, Cambridge.

ⓘ

Notes:: Cambridge Monographs on Mechanics and Applied Mathematics
External Links:: ISBN 0-521-22798-4, MathReview (Adelina Georgescu), ZentralBlatt
Referenced by:: (9.13.25), (9.13.27), (9.13.28), (9.13.29), (9.13.30), (9.13.35), (9.13.36), (9.13.37), Figure 9.13.1, Figure 9.13.1, Figure 9.13.2, Figure 9.13.2, §9.13(ii), §9.13(ii), §9.16.
Encodings:: BibTeX

…

10: Bibliography B

… ►

P. Baldwin (1991) Coefficient functions for an inhomogeneous turning-point problem. Mathematika 38 (2), pp. 217–238.

ⓘ

External Links:: ISSN 0025-5793, MathReview (Archibald D. MacGillivray), ZentralBlatt
Referenced by:: §2.8(iii).
Encodings:: BibTeX

… ►

W. G. Bickley (1935) Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

ⓘ

External Links:: Document, ZentralBlatt
Referenced by:: §10.73(iv).
Encodings:: BibTeX

… ►

Å. Björck (1996) Numerical Methods for Least Squares Problems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

ⓘ

External Links:: ISBN 0-89871-360-9, MathReview (Hongyuan Zha), ZentralBlatt
Referenced by:: §3.11(v).
Encodings:: BibTeX

… ►

P. Bleher and A. Its (1999) Semiclassical asymptotics of orthogonal polynomials, Riemann-Hilbert problem, and universality in the matrix model. Ann. of Math. (2) 150 (1), pp. 185–266.

ⓘ

External Links:: ISSN 0003-486X, Document, MathReview (Thomas Kriecherbauer), ZentralBlatt
Referenced by:: §18.32.
Encodings:: BibTeX

… ►

J. C. Bronski, L. D. Carr, B. Deconinck, J. N. Kutz, and K. Promislow (2001) Stability of repulsive Bose-Einstein condensates in a periodic potential. Phys. Rev. E (3) 63 (036612), pp. 1–11.

ⓘ

External Links:: Document
Referenced by:: §29.19(i).
Encodings:: BibTeX

…