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