solutions of differential equations

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11: Frank W. J. Olver

… ►He is particularly known for his extensive work in the study of the asymptotic solution of differential equations, i. …, the behavior of solutions as the independent variable, or some parameter, tends to infinity, and in the study of the particular solutions of differential equations known as special functions (e. …

12: Peter A. Clarkson

… ► Kruskal, he developed the “direct method” for determining symmetry solutions of partial differential equations in New similarity reductions of the Boussinesq equation (with M. …

13: 2.8 Differential Equations with a Parameter

§2.8 Differential Equations with a Parameter

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§2.8(i) Classification of Cases

… ►Zeros of $f(z)$ are also called turning points. … ►

§2.8(vi) Coalescing Transition Points

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14: Ronald F. Boisvert

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

15: Bonita V. Saunders

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

16: Bibliography O

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Exponentially improved asymptotic solutions of ordinary differential equations. II Irregular singularities of rank one. Proc. Roy. Soc. London Ser. A 445, pp. 39–56.

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External Links:

ISSN 0962-8444, FullText, MathReview (Hussain S. Nur), ZentralBlatt

Referenced by:

§13.4(i), §2.11(v), §2.7(ii).

Encodings:

BibTeX

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Exponentially-improved asymptotic solutions of ordinary differential equations I: The confluent hypergeometric function. SIAM J. Math. Anal. 24 (3), pp. 756–767.

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External Links:

ISSN 0036-1410, Document, MathReview (Hussain S. Nur), ZentralBlatt

Referenced by:

§10.17(v), §13.7(iii), (9.7.18), (9.7.19), (9.7.20), (9.7.21), (9.7.22), (9.7.23), §9.7(v).

Encodings:

BibTeX

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Asymptotic expansions of the coefficients in asymptotic series solutions of linear differential equations. Methods Appl. Anal. 1 (1), pp. 1–13.

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External Links:

ISSN 1073-2772, Pdf, MathReview (Archibald D. MacGillivray), ZentralBlatt

Referenced by:

§2.7(ii), §2.7(ii).

Encodings:

BibTeX

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Asymptotic solutions of linear ordinary differential equations at an irregular singularity of rank unity. Methods Appl. Anal. 4 (4), pp. 375–403.

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External Links:

ISSN 1073-2772, MathReview (A. D. Wood), ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

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On the uniqueness of asymptotic solutions of linear differential equations. Methods Appl. Anal. 6 (2), pp. 165–174.

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External Links:

ISSN 1073-2772, FullText, MathReview (P. K. Palamides), ZentralBlatt

Referenced by:

§2.7(ii).

Encodings:

BibTeX

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17: 4.34 Derivatives and Differential Equations

… ►With $a\ne 0$, the general solutions of the differential equations …

18: Howard S. Cohl

… ►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and $q$-series. …

19: 18.40 Methods of Computation

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20: 11.2 Definitions

… ►Particular solutions: … ►Particular solutions: … ►

§11.2(iii) Numerically Satisfactory Solutions

… ►(11.2.17) applies when $|\mathrm{ph}z|\le \frac{1}{2}\pi$ with $z$ bounded away from the origin.