differential equations

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11: 12.18 Methods of Computation

… ►These include the use of power-series expansions, recursion, integral representations, differential equations, asymptotic expansions, and expansions in series of Bessel functions. …

12: 32.13 Reductions of Partial Differential Equations

§32.13 Reductions of Partial Differential Equations

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13: Peter A. Clarkson

… ►Clarkson has published numerous papers on integrable systems (primarily Painlevé equations), special functions, and symmetry methods for differential equations. … Kruskal, he developed the “direct method” for determining symmetry solutions of partial differential equations in New similarity reductions of the Boussinesq equation (with M. …

14: 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. …

15: Bibliography O

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Hyperasymptotic solutions of second-order linear differential equations. II. Methods Appl. Anal. 2 (2), pp. 198–211.

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External Links:

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

Referenced by:

§10.17(v), §10.40(iv), §2.11(v), §9.7(v).

Encodings:

BibTeX

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Second-order linear differential equations with two turning points. Philos. Trans. Roy. Soc. London Ser. A 278, pp. 137–174.

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External Links:

FullText, MathReview (P. F. Hsieh), ZentralBlatt

Referenced by:

§2.8(vi).

Encodings:

BibTeX

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Second-order differential equations with fractional transition points. Trans. Amer. Math. Soc. 226, pp. 227–241.

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External Links:

FullText, MathReview (Anthony Leung), ZentralBlatt

Referenced by:

§2.8(v).

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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Applications of Lie Groups to Differential Equations. 2nd edition, Graduate Texts in Mathematics, Vol. 107, Springer-Verlag, New York.

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External Links:

ISBN 0-387-94007-3; 0-387-95000-1, MathReview, ZentralBlatt

Referenced by:

§32.13(i).

Encodings:

BibTeX

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16: 36.15 Methods of Computation

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§36.15(v) Differential Equations

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

17: 1.13 Differential Equations

§1.13 Differential Equations

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Fundamental Pair

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Wronskian

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§1.13(iii) Inhomogeneous Equations

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18: 2.7 Differential Equations

§2.7 Differential Equations

… ►An ordinary point of the differential equation … ►

§2.7(ii) Irregular Singularities of Rank 1

… ►See §2.11(v) for other examples. … ►

§2.7(iv) Numerically Satisfactory Solutions

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19: 15.17 Mathematical Applications

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§15.17(i) Differential Equations

… ►The three singular points in Riemann’s differential equation (15.11.1) lead to an interesting Riemann sheet structure. …These monodromy groups are finite iff the solutions of Riemann’s differential equation are all algebraic. …

20: Gerhard Wolf

… ► Schmidt) of the Chapter Double Confluent Heun Equation in the book Heun’s Differential Equations (A. …