integrable differential equations
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11—20 of 85 matching pages
11: 4.45 Methods of Computation
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►Initial approximations are obtainable, for example, from the power series (4.13.6) (with ) when is close to , from the asymptotic expansion (4.13.10) when is large, and by numerical integration of the differential equation (4.13.4) (§3.7) for other values of .
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12: Peter A. Clarkson
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►Clarkson has published numerous papers on integrable systems (primarily Painlevé equations), special functions, and symmetry methods for differential equations.
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13: Alexander I. Bobenko
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►Bobenko’s books are Algebro-geometric Approach to Nonlinear Integrable Problems (with E.
… Matveev), published by Springer in 1994, Painlevé Equations in the Differential Geometry of
Surfaces (with U.
Eitner), published by Springer in 2000, and Discrete Differential Geometry: Integrable Structure (with Y.
…He is also coeditor of Discrete Integrable Geometry and Physics (with R.
Seiler), published by Oxford University Press in 1999, and Discrete Differential Geometry (with P.
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14: 23.21 Physical Applications
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►Airault et al. (1977) applies the function to an integrable classical many-body problem, and relates the solutions to nonlinear partial differential equations.
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15: Bibliography L
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Well-posedness and blow-up solutions for an integrable nonlinearly dispersive model wave equation.
J. Differential Equations 162 (1), pp. 27–63.
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16: 16.25 Methods of Computation
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►Methods for computing the functions of the present chapter include power series, asymptotic expansions, integral representations, differential equations, and recurrence relations.
…There is, however, an added feature in the numerical solution of differential equations and difference equations (recurrence relations).
…In these cases integration, or recurrence, in either a forward or a backward direction is unstable.
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17: 3.7 Ordinary Differential Equations
§3.7 Ordinary Differential Equations
… ► … ►§3.7(ii) Taylor-Series Method: Initial-Value Problems
… ► … ►§3.7(v) Runge–Kutta Method
…18: 9.12 Scorer Functions
19: 1.17 Integral and Series Representations of the Dirac Delta
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►In the language of physics and applied mathematics, these equations indicate the normalizations chosen for these non- improper eigenfunctions of the differential operators (with derivatives respect to spatial co-ordinates) which generate them; the normalizations (1.17.12_1) and (1.17.12_2) are explicitly derived in Friedman (1990, Ch. 4), the others follow similarly.
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