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21: Bibliography L

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Numerical Solution of Linear Difference Equations. NBSIR Technical Report 80-1976, National Bureau of Standards, Gaithersburg, MD 20899.

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Notes:

(Available from National Technical Information Service, Springfield, VA 22161.)

Referenced by:

§16.25, §3.6(vii).

Encodings:

BibTeX

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22: Bibliography

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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

External Links:

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

Referenced by:

§3.7(iii).

Encodings:

BibTeX

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23: 13.14 Definitions and Basic Properties

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§13.14(v) Numerically Satisfactory Solutions

►Fundamental pairs of solutions of (13.14.1) that are numerically satisfactory (§2.7(iv)) in the neighborhood of infinity are … ►A fundamental pair of solutions that is numerically satisfactory in the sector $|\mathrm{ph}z|\le \pi$ near the origin is …

24: 10.47 Definitions and Basic Properties

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§10.47(iii) Numerically Satisfactory Pairs of Solutions

►For (10.47.1) numerically satisfactory pairs of solutions are given by Table 10.2.1 with the symbols $J$, $Y$, $H$, and $\nu$ replaced by $𝗃$, $𝗒$, $𝗁$, and $n$, respectively. ►For (10.47.2) numerically satisfactory pairs of solutions are ${𝗂}_n^{(1)}\left(z\right)$ and ${𝗄}_n\left(z\right)$ in the right half of the $z$-plane, and ${𝗂}_n^{(1)}\left(z\right)$ and ${𝗄}_n\left(-z\right)$ in the left half of the $z$-plane. …

25: 12.2 Differential Equations

… ►All solutions are entire functions of $z$ and entire functions of $a$ or $\nu$. ►For real values of $z$ $(=x)$, numerically satisfactory pairs of solutions (§2.7(iv)) of (12.2.2) are $U(a,x)$ and $V(a,x)$ when $x$ is positive, or $U(a,-x)$ and $V(a,-x)$ when $x$ is negative. … ►In $ℂ$, for $j=0,1,2,3$, $U({(-1)}^{j-1}a,{(-\mathrm{i})}^{j-1}z)$ and $U({(-1)}^{j}a,{(-\mathrm{i})}^{j}z)$ comprise a numerically satisfactory pair of solutions in the half-plane $\frac{1}{4}(2j-3)\pi \le \mathrm{ph}z\le \frac{1}{4}(2j+1)\pi$. …

26: 9.12 Scorer Functions

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§9.12(iv) Numerically Satisfactory Solutions

… ►In $ℂ$, numerically satisfactory sets of solutions are given by …

27: Bibliography C

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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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External Links:

MathReview (L. Fox), ZentralBlatt

Referenced by:

§18.38(i), §3.11(ii).

Encodings:

BibTeX

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28: 31.18 Methods of Computation

… ►Independent solutions of (31.2.1) can be computed in the neighborhoods of singularities from their Fuchs–Frobenius expansions (§31.3), and elsewhere by numerical integration of (31.2.1). Subsequently, the coefficients in the necessary connection formulas can be calculated numerically by matching the values of solutions and their derivatives at suitably chosen values of $z$; see Laĭ (1994) and Lay et al. (1998). …

29: Mathematical Introduction

… ►These include, for example, multivalued functions of complex variables, for which new definitions of branch points and principal values are supplied (§§1.10(vi), 4.2(i)); the Dirac delta (or delta function), which is introduced in a more readily comprehensible way for mathematicians (§1.17); numerically satisfactory solutions of differential and difference equations (§§2.7(iv), 2.9(i)); and numerical analysis for complex variables (Chapter 3). …

30: 12.14 The Function $W(a,x)$

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§12.14(i) Introduction

… ► $W(a,x)$ and $W(a,-x)$ form a numerically satisfactory pair of solutions when . …