numerical solutions

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1: 16.25 Methods of Computation

… ►There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations). …

2: 3.6 Linear Difference Equations

§3.6 Linear Difference Equations

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§3.6(ii) Homogeneous Equations

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§3.6(iv) Inhomogeneous Equations

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3: 3.7 Ordinary Differential Equations

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§3.7(ii) Taylor-Series Method: Initial-Value Problems

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§3.7(iii) Taylor-Series Method: Boundary-Value Problems

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§3.7(v) Runge–Kutta Method

… ►An extensive literature exists on the numerical solution of ordinary differential equations by Runge–Kutta, multistep, or other methods. …

4: Ronald F. Boisvert

… ►His research interests include numerical solution of partial differential equations, mathematical software, and information services that support computational science. …

5: Bonita V. Saunders

… ►Her research interests include numerical grid generation, numerical solution of partial differential equations, and visualization of special functions. …

6: 36.15 Methods of Computation

… ►For numerical solution of partial differential equations satisfied by the canonical integrals see Connor et al. (1983).

7: 18.38 Mathematical Applications

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Differential Equations: Spectral Methods

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Quadrature “Extended” to Pseudo-Spectral (DVR) Representations of Operators in One and Many Dimensions

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8: Bibliography O

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On the asymptotic and numerical solution of linear ordinary differential equations. SIAM Rev. 40 (3), pp. 463–495.

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External Links:

ISSN 1095-7200, Document, MathReview (W. Balser), ZentralBlatt

Referenced by:

§16.25, §2.7(ii), §3.7(iii).

Encodings:

BibTeX

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Error bounds for asymptotic solutions of second-order differential equations having an irregular singularity of arbitrary rank. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 244–249.

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External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

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On the asymptotic solution of second-order differential equations having an irregular singularity of rank one, with an application to Whittaker functions. J. Soc. Indust. Appl. Math. Ser. B Numer. Anal. 2 (2), pp. 225–243.

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External Links:

Document, MathReview (T. E. Hull), ZentralBlatt

Referenced by:

§13.19, §13.7(ii).

Encodings:

BibTeX

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Numerical solution of second-order linear difference equations. J. Res. Nat. Bur. Standards Sect. B 71B, pp. 111–129.

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External Links:

MathReview (G. N. Lance), ZentralBlatt

Referenced by:

§3.6(iv), §3.6(v).

Encodings:

BibTeX

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

Encodings:

BibTeX

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9: 14.21 Definitions and Basic Properties

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§14.21(ii) Numerically Satisfactory Solutions

►When $\mathrm{\Re }\nu \ge -\frac{1}{2}$ and $\mathrm{\Re }\mu \ge 0$, a numerically satisfactory pair of solutions of (14.21.1) in the half-plane $|\mathrm{ph}z|\le \frac{1}{2}\pi$ is given by $P_{\nu }^{-\mu }\left(z\right)$ and ${𝑸}_{\nu }^{\mu }\left(z\right)$. …

10: 3.8 Nonlinear Equations

§3.8 Nonlinear Equations

… ►Corresponding numerical factors in this example for other zeros and other values of $j$ are obtained in Gautschi (1984, §4). …