ordinary differential equations

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11: 22.19 Physical Applications

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§22.19(iii) Nonlinear ODEs and PDEs

►Many nonlinear ordinary and partial differential equations have solutions that may be expressed in terms of Jacobian elliptic functions. …

12: Bibliography B

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Ordinary differential equations. Fourth edition, John Wiley & Sons, Inc., New York.

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External Links:

ISBN 0-471-86003-4, MathReview (Michal Čverčko)

Referenced by:

§1.13(viii), §1.13(viii), §1.18(iv).

Encodings:

BibTeX

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The Numerical Analysis of Ordinary Differential Equations. Runge-Kutta and General Linear Methods. John Wiley & Sons Ltd., Chichester.

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External Links:

ISBN 0-471-91046-5, MathReview (Peter Alfeld), ZentralBlatt

Referenced by:

§3.7(v).

Encodings:

BibTeX

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Numerical Methods for Ordinary Differential Equations. John Wiley & Sons Ltd., Chichester.

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External Links:

ISBN 0-471-96758-0, MathReview (Ian Gladwell), ZentralBlatt

Referenced by:

§32.17.

Encodings:

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13: 2.7 Differential Equations

… ►An ordinary point of the differential equation …All solutions are analytic at an ordinary point, and their Taylor-series expansions are found by equating coefficients. …

14: Bibliography W

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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.

External Links:

MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

Ch.2, Ch.9.

Encodings:

BibTeX

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15: 18.38 Mathematical Applications

… ►Linear ordinary differential equations can be solved directly in series of Chebyshev polynomials (or other OP’s) by a method originated by Clenshaw (1957). …

16: 1.13 Differential Equations

… ►A standard form for second order ordinary differential equations with $x\in ℝ$, and with a real parameter $\lambda$, and real valued functions $p(x),q(x),$ and $\rho (x)$, with $p(x)$ and $\rho (x)$ positive, is …

17: Bibliography C

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

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External Links:

MathReview (M. Zlámal)

Referenced by:

§1.18(ix), §1.18(x).

Encodings:

BibTeX

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18: Bibliography M

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Hyperasymptotic solutions of second-order ordinary differential equations with a singularity of arbitrary integer rank. Methods Appl. Anal. 4 (3), pp. 250–260.

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External Links:

ISSN 1073-2772, MathReview (W. Balser), ZentralBlatt

Referenced by:

§2.11(v).

Encodings:

BibTeX

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19: 3.11 Approximation Techniques

… ►Also, in cases where $f(x)$ satisfies a linear ordinary differential equation with polynomial coefficients, the expansion (3.11.11) can be substituted in the differential equation to yield a recurrence relation satisfied by the $c_n$. …

20: 18.39 Applications in the Physical Sciences

… ►Substitution of (18.39.24) into (18.39.23) then gives the ordinary differential equation for the radial wave function $R_{n,l}(r)$, …