numerically%20satisfactory%20solutions

SearchAdvancedHelp

(0.003 seconds)

11—20 of 368 matching pages

11: Bibliography O

… ►

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

ⓘ

External Links:

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

Referenced by:

§16.25, §2.7(ii), §3.7(iii).

Encodings:

BibTeX

… ►

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.

ⓘ

External Links:

Document, MathReview, ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

… ►

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.

ⓘ

External Links:

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

Referenced by:

§13.19, §13.7(ii).

Encodings:

BibTeX

►

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

ⓘ

External Links:

MathReview (G. N. Lance), ZentralBlatt

Referenced by:

§3.6(iv), §3.6(v).

Encodings:

BibTeX

… ►

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

ⓘ

External Links:

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

Referenced by:

§32.17, §32.17.

Encodings:

BibTeX

…

12: 2.11 Remainder Terms; Stokes Phenomenon

… ►

§2.11(i) Numerical Use of Asymptotic Expansions

… ►

§2.11(vi) Direct Numerical Transformations

… ►The numerically smallest terms are the 5th and 6th. … ►For example, using double precision $d_{20}$ is found to agree with (2.11.31) to 13D. ►However, direct numerical transformations need to be used with care. …

13: 15.10 Hypergeometric Differential Equation

… ►

§15.10(i) Fundamental Solutions

… ►They are also numerically satisfactory (§2.7(iv)) in the neighborhood of the corresponding singularity. … ► ►

§15.10(ii) Kummer’s 24 Solutions and Connection Formulas

… ►The $\left(\genfrac{}{}{0.0pt}{}{6}{3}\right)=20$ connection formulas for the principal branches of Kummer’s solutions are: …

14: 3.8 Nonlinear Equations

§3.8 Nonlinear Equations

… ►Because the method requires only one function evaluation per iteration, its numerical efficiency is ultimately higher than that of Newton’s method. … ►Consider $x=20$ and $j=19$. We have $p^{\prime }(20)=19!$ and $a_{19}=1+2+\mathrm{\cdots }+20=210$. … ►Corresponding numerical factors in this example for other zeros and other values of $j$ are obtained in Gautschi (1984, §4). …

15: 10.2 Definitions

… ►

§10.2(ii) Standard Solutions

… ►This solution of (10.2.1) is an analytic function of $z\in ℂ$, except for a branch point at $z=0$ when $\nu$ is not an integer. … ►Each solution has a branch point at $z=0$ for all $\nu \in ℂ$. … ►

§10.2(iii) Numerically Satisfactory Pairs of Solutions

►Table 10.2.1 lists numerically satisfactory pairs of solutions (§2.7(iv)) of (10.2.1) for the stated intervals or regions in the case $\mathrm{\Re }\nu \ge 0$. …

16: 31.18 Methods of Computation

§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). Care needs to be taken to choose integration paths in such a way that the wanted solution is growing in magnitude along the path at least as rapidly as all other solutions (§3.7(ii)). …

17: 11.2 Definitions

… ►

§11.2(iii) Numerically Satisfactory Solutions

… ►When $z=x$, , and $\mathrm{\Re }\nu \ge 0$, numerically satisfactory general solutions of (11.2.7) are given by … ►When $z\in ℂ$ and $\mathrm{\Re }\nu \ge 0$, numerically satisfactory general solutions of (11.2.7) are given by … ►When $\mathrm{\Re }\nu \ge 0$, numerically satisfactory general solutions of (11.2.9) are given by …(11.2.17) applies when $|\mathrm{ph}z|\le \frac{1}{2}\pi$ with $z$ bounded away from the origin.

18: Tom M. Apostol

… ►Apostol was born on August 20, 1923. … ►His complete list of publications contains numerous articles and research papers (fifty of them published since he became Emeritus in 1992), as well as sixty-one books, sixteen videotapes, and nine DVD’s. …

19: Bibliography I

… ►

The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of $J_0(z)-i{J}_1(z)$ and of Bessel functions $J_m(z)$ of any real order $m$ . Linear Algebra Appl. 194, pp. 35–70.

ⓘ

External Links:

ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt

Referenced by:

§10.21(ix).

Encodings:

BibTeX

… ►

The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

ⓘ

External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX

… ►

Highly Oscillatory Quadrature: The Story So Far. In Numerical Mathematics and Advanced Applications, A. Bermudez de Castro and others (Eds.), pp. 97–118.

ⓘ

Notes:

Proceedings of ENuMath, Santiago de Compostela (2005)

External Links:

ISBN 3-540-34287-7, MathReview, ZentralBlatt

Referenced by:

§3.5(vii).

Encodings:

BibTeX

►

A First Course in the Numerical Analysis of Differential Equations. Cambridge Texts in Applied Mathematics, No. 15, Cambridge University Press, Cambridge.

ⓘ

External Links:

ISBN 0-521-55376-8; 0-521-55655-4, MathReview (Luis Verde-Star), ZentralBlatt

Referenced by:

§3.7(i).

Encodings:

BibTeX

… ►

More on electrostatic models for zeros of orthogonal polynomials. Numer. Funct. Anal. Optim. 21 (1-2), pp. 191–204.

ⓘ

External Links:

ISSN 0163-0563, FullText, MathReview (M. E. Muldoon), ZentralBlatt

Referenced by:

§18.39(v).

Encodings:

BibTeX

…

20: 3.4 Differentiation

… ► ►

§3.4(ii) Analytic Functions

… ►

Laplacian

… ►

Biharmonic Operator

… ►