differential equations

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21: 32.17 Methods of Computation

… ►The Painlevé equations can be integrated by Runge–Kutta methods for ordinary differential equations; see §3.7(v), Hairer et al. (2000), and Butcher (2003). …

22: T. Mark Dunster

… ►He has received a number of National Science Foundation grants, and has published numerous papers in the areas of uniform asymptotic solutions of differential equations, convergent WKB methods, special functions, quantum mechanics, and scattering theory. …

23: Daniel W. Lozier

… ►Army Engineer Research and Development Laboratory in Virginia on finite-difference solutions of differential equations associated with nuclear weapons effects. Then he transferred to NIST (then known as the National Bureau of Standards), where he collaborated for several years with the Building and Fire Research Laboratory developing and applying finite-difference and spectral methods to differential equation models of fire growth. …

24: 16.8 Differential Equations

§16.8 Differential Equations

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§16.8(i) Classification of Singularities

►An ordinary point of the differential equation … … ►

§16.8(ii) The Generalized Hypergeometric Differential Equation

…

25: 4.7 Derivatives and Differential Equations

§4.7 Derivatives and Differential Equations

… ►For a nonvanishing analytic function $f(z)$, the general solution of the differential equation … ►The general solution of the differential equation … ►The general solution of the differential equation … ►For other differential equations see Kamke (1977, pp. 396–413).

26: 16.21 Differential Equation

§16.21 Differential Equation

► $w=G_{p,q}^{m,n}(z;𝐚;𝐛)$ satisfies the differential equation …

27: 9.17 Methods of Computation

… ►

§9.17(ii) Differential Equations

►A comprehensive and powerful approach is to integrate the defining differential equation (9.2.1) by direct numerical methods. As described in §3.7(ii), to ensure stability the integration path must be chosen in such a way that as we proceed along it the wanted solution grows at least as fast as all other solutions of the differential equation. … ►In the case of the Scorer functions, integration of the differential equation (9.12.1) is more difficult than (9.2.1), because in some regions stable directions of integration do not exist. …

28: 21.9 Integrable Equations

§21.9 Integrable Equations

►Riemann theta functions arise in the study of integrable differential equations that have applications in many areas, including fluid mechanics (Ablowitz and Segur (1981, Chapter 4)), magnetic monopoles (Ercolani and Sinha (1989)), and string theory (Deligne et al. (1999, Part 3)). … ►

29: 4.34 Derivatives and Differential Equations

§4.34 Derivatives and Differential Equations

… ►With $a\ne 0$, the general solutions of the differential equations … ►For other differential equations see Kamke (1977, pp. 289–400).

30: 4.20 Derivatives and Differential Equations

§4.20 Derivatives and Differential Equations

… ►With $a\ne 0$, the general solutions of the differential equations … ►For other differential equations see Kamke (1977, pp. 355–358 and 396–400).