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32 Painlevé TranscendentsComputation

§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). For numerical studies of PI see Holmes and Spence (1984), Noonburg (1995), and Fornberg and Weideman (2011). For numerical studies of PII see Rosales (1978), Miles (1978, 1980), Kashevarov (1998, 2004), and S. Olver (2011). For numerical studies of PIV see Bassom et al. (1993).