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1: Bibliography B

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Bessel functions and modular relations of higher type and hyperbolic differential equations. Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (Tome Supplementaire), pp. 12–20.

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MathReview (S. C. van Veen), ZentralBlatt

Referenced by:

§35.5(i).

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2: Bibliography D

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Stability of Runge-Kutta Methods for Stiff Nonlinear Differential Equations. CWI Monographs, Vol. 2, North-Holland Publishing Co., Amsterdam.

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ISBN 0-444-87634-0, MathReview (A. de Castro Brzezicki), ZentralBlatt

Referenced by:

§3.7(v).

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Error bounds for exponentially improved asymptotic solutions of ordinary differential equations having irregular singularities of rank one. Methods Appl. Anal. 3 (1), pp. 109–134.

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ISSN 1073-2772, Pdf, MathReview (Roderick Wong), ZentralBlatt

Referenced by:

§2.11(v).

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Convergent expansions for solutions of linear ordinary differential equations having a simple turning point, with an application to Bessel functions. Stud. Appl. Math. 107 (3), pp. 293–323.

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ISSN 0022-2526, Document, MathReview, ZentralBlatt

Referenced by:

§10.20(ii), §2.8(i).

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Olver’s error bound methods applied to linear ordinary differential equations having a simple turning point. Anal. Appl. (Singap.) 12 (4), pp. 385–402.

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ISSN 0219-5305, Document, Link, MathReview (Thomas Mbah Acho), ZentralBlatt

Referenced by:

5th item, §14.32.

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A survey on orthogonal matrix polynomials satisfying second order differential equations. J. Comput. Appl. Math. 178 (1-2), pp. 169–190.

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ISSN 0377-0427, Document, MathReview, ZentralBlatt

Referenced by:

§18.36(iv).

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3: Bibliography V

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A Mathieu equation for ships rolling among waves. I, II. Norske Vid. Selsk. Forh., Trondheim 22 (25–26), pp. 113–123.

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MathReview (J. V. Wehausen), ZentralBlatt

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2nd item.

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On the growth of convergence radii for the eigenvalues of the Mathieu equation. Math. Nachr. 192, pp. 239–253.

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ISSN 0025-584X, Document, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§28.6(i).

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Error estimates for Rayleigh-Ritz approximations of eigenvalues and eigenfunctions of the Mathieu and spheroidal wave equation. Constr. Approx. 20 (1), pp. 39–54.

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ISSN 0176-4276, Document, MathReview, ZentralBlatt

Referenced by:

§30.16(i), §30.16(ii), §30.16(ii).

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Approximation of eigenvalues of some differential equations by zeros of orthogonal polynomials. J. Comput. Appl. Math. 213 (2), pp. 488–500.

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ISSN 0377-0427, Document, FullText, MathReview (Javier Segura), ZentralBlatt

Referenced by:

item (f), §28.34(ii), §29.20(i).

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On the rational solutions of the second Painlevé equation. Differ. Uravn. 1 (1), pp. 79–81 (Russian).

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Notes:

In Russian. English translation: Differential Equations 1(1), pp. 58–59.

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MathReview, ZentralBlatt

Referenced by:

§32.8(ii).

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4: Bibliography L

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The two-point connection problem for differential equations of the Heun class. Teoret. Mat. Fiz. 101 (3), pp. 360–368 (Russian).

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Notes:

In Russian. English translation: Theoret. and Math. Phys. 101(1994), no. 3, pp. 1413–1418 (1995)

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ISSN 0564-6162, Document, MathReview, ZentralBlatt

Referenced by:

§31.18.

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Some differential equations and associated integral equations. Quart. J. Math. (Oxford) 5, pp. 81–97.

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Document, ZentralBlatt

Referenced by:

§31.10(i), §31.9(i).

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Algorithm 537: Characteristic values of Mathieu’s differential equation. ACM Trans. Math. Software 5 (1), pp. 112–117.

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ISSN 0098-3500, Document, GAMS (module 537; package TOMS)

Referenced by:

2nd item, 2nd item.

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Some Differential Equations Satisfied by Hypergeometric Functions. In Approximation and Computation (West Lafayette, IN, 1993), Internat. Ser. Numer. Math., Vol. 119, pp. 371–381.

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MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§16.8(ii).

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The second Painlevé equation. Differ. Uravn. 7 (6), pp. 1124–1125 (Russian).

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Notes:

In Russian. English translation: Differential Equations 7(6), pp. 853–854

External Links:

MathReview (Z. Rubinstein), ZentralBlatt

Referenced by:

§32.7(ii).

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5: Bibliography K

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Asymptotic behavior of the solutions of the Painlevé equation of the first kind. Differ. Uravn. 24 (10), pp. 1684–1695 (Russian).

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Notes:

In Russian. English translation: Differential Equations 24(1988), no. 10, pp. 1107–1115 (1989)

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ISSN 0374-0641, MathReview, ZentralBlatt

Referenced by:

§32.11(i).

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Rational solutions of the fifth Painlevé equation. Differential Integral Equations 7 (3-4), pp. 967–1000.

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ISSN 0893-4983, MathReview, ZentralBlatt

Referenced by:

§32.8(v).

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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I. Inverse Problems 20 (4), pp. 1165–1206.

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ISSN 0266-5611, Document, MathReview (Shun Shimomura), ZentralBlatt

Referenced by:

§32.11(iv).

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On differential equations for Sobolev-type Laguerre polynomials. Trans. Amer. Math. Soc. 350 (1), pp. 347–393.

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ISSN 0002-9947, FullText, MathReview (Hans W. Volkmer), ZentralBlatt

Referenced by:

§18.36(ii).

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An algorithm for solving second order linear homogeneous differential equations. J. Symbolic Comput. 2 (1), pp. 3–43.

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ISSN 0747-7171, MathReview, ZentralBlatt

Referenced by:

§31.14(ii).

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6: Bibliography S

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Time propagation of partial differential equations using the short iterative Lanczos method and finite-element discrete variable representation. Adv. Quantum Chem. 72, pp. 95–127.

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Referenced by:

§18.38(i).

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The computation of eigenvalues and solutions of Mathieu’s differential equation for noninteger order. ACM Trans. Math. Software 19 (3), pp. 377–390.

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ISSN 0098-3500, Document, ZentralBlatt

Referenced by:

item (e).

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Differential Equations with Applications and Historical Notes. McGraw-Hill Book Co., New York.

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Notes:

International Series in Pure and Applied Mathematics

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MathReview (J. S. Joel), ZentralBlatt

Referenced by:

§1.13(iii).

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The linear differential equation whose solutions are the products of solutions of two given differential equations. J. Math. Anal. Appl. 98 (1), pp. 130–147.

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ISSN 0022-247X, Document, FullText, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§1.13(v).

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Error bounds for asymptotic solutions of differential equations. I. The distinct eigenvalue case. J. Res. Nat. Bur. Standards Sect. B 70B, pp. 167–186.

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MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§2.7(ii).

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7: Bibliography C

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Elementary Differential Equations. Clarendon Press, Oxford.

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ISBN 0-19-853139-7, MathReview, ZentralBlatt

Referenced by:

§16.12.

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Algorithm 352: Characteristic values and associated solutions of Mathieu’s differential equation. Comm. ACM 12 (7), pp. 399–407.

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Notes:

Includes double-precision Fortran program, maximum accuracy 13D.

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ISSN 0001-0782, Document

Referenced by:

§28.36(ii), §28.36(iii).

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The numerical solution of linear differential equations in Chebyshev series. Proc. Cambridge Philos. Soc. 53 (1), pp. 134–149.

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MathReview (L. Fox), ZentralBlatt

Referenced by:

§18.38(i), §3.11(ii).

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Theory of ordinary differential equations. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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MathReview (M. Zlámal)

Referenced by:

§1.18(ix), §1.18(x).

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Coulomb effects in the Klein-Gordon equation for pions. Phys. Rev. C 20 (2), pp. 696–704.

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Document

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5th item.

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8: 10.73 Physical Applications

… ► … ► … ►See Krivoshlykov (1994, Chapter 2, §2.2.10; Chapter 5, §5.2.2), Kapany and Burke (1972, Chapters 4–6; Chapter 7, §A.1), and Slater (1942, Chapter 4, §§20, 25). … ►In the theory of plates and shells, the oscillations of a circular plate are determined by the differential equation …

9: Bibliography W

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Linear difference equations with transition points. Math. Comp. 74 (250), pp. 629–653.

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ISSN 0025-5718, Document, MathReview (B. G. Pachpatte), ZentralBlatt

Referenced by:

§2.9(iii).

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The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt

Referenced by:

§29.19(ii).

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Asymptotic Expansions for Ordinary Differential Equations. Interscience Publishers John Wiley & Sons, Inc., New York-London-Sydney.

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Notes:

Reprinted by Krieger, New York, 1976 and Dover, New York, 1987.

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MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

Ch.2, Ch.9.

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Solutions of the fifth Painlevé equation. I. Hokkaido Math. J. 24 (2), pp. 231–267.

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ISSN 0385-4035, FullText, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.10(v).

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Asymptotic solutions of a fourth order differential equation. Stud. Appl. Math. 118 (2), pp. 133–152.

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ISSN 0022-2526, Document, MathReview Entry

Referenced by:

§2.8(vi).

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10: Bibliography G

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The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals. Ann. of Math. (2) 48 (4), pp. 785–826.

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FullText, MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§35.2, §35.3(ii).

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Computing solutions of the modified Bessel differential equation for imaginary orders and positive arguments. ACM Trans. Math. Software 30 (2), pp. 145–158.

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ISSN 0098-3500, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(viii).

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Linear Differential Equations and Group Theory from Riemann to Poincaré. 2nd edition, Birkhäuser Boston Inc., Boston, MA.

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ISBN 0-8176-3837-7, MathReview, ZentralBlatt

Referenced by:

§15.17(v).

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Special classes of solutions of Painlevé equations. Differ. Uravn. 18 (3), pp. 419–429 (Russian).

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Notes:

In Russian. English translation: Differential Equations 18(3), pp. 317–326.

External Links:

ISSN 0374-0641, MathReview, ZentralBlatt

Referenced by:

§32.10(iv), §32.10(v), §32.8(iii), §32.8(v), §32.9(ii).

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Theory of Painlevé’s equations. Differ. Uravn. 11 (11), pp. 373–376 (Russian).

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Notes:

In Russian. English translation: Differential Equations 11(11), pp. 285–287

External Links:

MathReview (Z. Nehari), ZentralBlatt

Referenced by:

§32.7(iii), §32.7(vi).

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