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11: Bibliography H

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The combination of $R$-matrix and complex coordinate methods: Application to the diamagnetic Rydberg spectra of Ba and Sr. J. Phys. B 26 (12), pp. 1775–1790.

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ISSN 0953-4075, Document, MathReview

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4th item.

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A boundary value problem associated with the second Painlevé transcendent and the Korteweg-de Vries equation. Arch. Rational Mech. Anal. 73 (1), pp. 31–51.

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ISSN 0003-9527, Document, MathReview (Richard Brown), ZentralBlatt

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§32.11(ii).

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On a Painlevé-type boundary-value problem. Quart. J. Mech. Appl. Math. 37 (4), pp. 525–538.

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ISSN 0033-5614, Document, MathReview, ZentralBlatt

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§32.11(i), §32.17.

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12: Bibliography J

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Methods of Mathematical Physics. 3rd edition, Cambridge University Press, Cambridge.

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Notes:

Reprinted in 1999.

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MathReview, ZentralBlatt

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§10.1, §12.17, Ch.14, Ch.6, §7.18(iv), Ch.9, Notations H, Notations H, Notations K.

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Asymptotics of the hypergeometric function. Math. Methods Appl. Sci. 24 (6), pp. 369–389.

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ISSN 0170-4214, Document, MathReview, ZentralBlatt

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§14.15(iii), §15.12(iii).

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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.

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ISSN 0075-4102, Document, MathReview (Mehmet Can), ZentralBlatt

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§32.11(i).

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13: 14.31 Other Applications

… ►The conical functions ${𝖯}_{-\frac{1}{2}+\mathrm{i}\tau }^m\left(x\right)$ appear in boundary-value problems for the Laplace equation in toroidal coordinates (§14.19(i)) for regions bounded by cones, by two intersecting spheres, or by one or two confocal hyperboloids of revolution (Kölbig (1981)). …

14: 28.33 Physical Applications

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Boundary-values problems arising from solution of the two-dimensional wave equation in elliptical coordinates. This yields a pair of equations of the form (28.2.1) and (28.20.1), and the appropriate solution of (28.2.1) is usually a periodic solution of integer order. See §28.33(ii).

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§28.33(ii) Boundary-Value Problems

… ►For a visualization see Gutiérrez-Vega et al. (2003), and for references to other boundary-value problems see: …

15: Bibliography S

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A global Newton method for the zeros of cylinder functions. Numer. Algorithms 18 (3-4), pp. 259–276.

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ISSN 1017-1398, Document, MathReview, ZentralBlatt

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§10.74(vi).

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Practical Extrapolation Methods: Theory and Applications. Cambridge Monographs on Applied and Computational Mathematics, Vol. 10, Cambridge University Press, Cambridge.

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ISBN 0-521-66159-5, MathReview (Thomas A. Atchison), ZentralBlatt

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§3.9(vi).

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Some Boundary Value Problems Associated with the Heun Equation. Ph.D. Thesis, London University.

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Available from the library, University of Surrey, UK

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LibraryRecord

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§31.9(i), §31.9(ii), Ch.31, Profile Brian D. Sleeman.

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Mixed Boundary Value Problems in Potential Theory. North-Holland Publishing Co., Amsterdam.

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MathReview (R. Shail), ZentralBlatt

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§10.22(iv).

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Numerical Methods Based on Sinc and Analytic Functions. Springer Series in Computational Mathematics, Vol. 20, Springer-Verlag, New York.

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Sinc-Pack, a set of 480 Matlab programs with a 470-page tutorial, is available for purchase from SINC, LLC by contacting Frank Stenger.

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ISBN 0-387-94008-1, MathReview (B. Boyanov), ZentralBlatt

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§3.3(vi), §3.4(i), §3.5(i).

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16: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►Ignoring the boundary value terms it follows that … ► A boundary value for the end point $a$ is a linear form $ℬ$ on $𝒟({ℒ}^{\ast })$ of the form …Boundary values and boundary conditions for the end point $b$ are defined in a similar way. If $n_1=1$ then there are no nonzero boundary values at $a$; if $n_1=2$ then the above boundary values at $a$ form a two-dimensional class. … ►The reader is referred to Coddington and Levinson (1955), Friedman (1990, Ch. 3), Titchmarsh (1962a), and Everitt (2005b, pp. 45–74) and Everitt (2005a, pp. 272–331), for detailed methods and results. …

17: Bibliography

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The $J$-Matrix Method. Developments and Applications. Springer-Verlag.

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ISBN 978-1-4020-6072-4

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§18.39(iv).

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Pfaff’s method II: Diverse applications. J. Comput. Appl. Math. 68 (1-2), pp. 15–23.

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ISSN 0377-0427, Document, MathReview (Bruce C. Berndt), ZentralBlatt

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§17.7(iii).

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On magic squares constructed by the uniform step method. Proc. Amer. Math. Soc. 2 (4), pp. 557–565.

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ISSN 0002-9939, Fulltext, MathReview (D. H. Lehmer), ZentralBlatt

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§27.17.

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Mathematical Methods for Physicists. 6th edition, Elsevier, Oxford.

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ISBN 0-12-059876-0;0-12-088584-0, MathReview, ZentralBlatt

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§1.17(ii), §1.17(iii).

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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations. Classics in Applied Mathematics, Vol. 13, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

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Notes:

Corrected reprint of the 1988 original

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ISBN 0-89871-354-4, MathReview, ZentralBlatt

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§3.7(iii).

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18: 30.13 Wave Equation in Prolate Spheroidal Coordinates

… ►For the Dirichlet boundary-value problem of the region ${\xi }_1\le \xi \le {\xi }_2$ between two ellipsoids, the eigenvalues are determined from …

19: 3.8 Nonlinear Equations

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Bisection Method

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Secant Method

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Steffensen’s Method

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Eigenvalue Methods

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20: 27.15 Chinese Remainder Theorem

… ►Their product $m$ has 20 digits, twice the number of digits in the data. …These numbers, in turn, are combined by the Chinese remainder theorem to obtain the final result $(modm)$, which is correct to 20 digits. … ►Details of a machine program describing the method together with typical numerical results can be found in Newman (1967). …