§32.17 Methods of Computation

Keywords:: Painlevé transcendents
Permalink:: http://dlmf.nist.gov/32.17

The Painlevé equations can be integrated by Runge–Kutta methods for ordinary differential equations; see §3.7(v), Butcher (2003), and Hairer et al. (2000). For numerical studies of $\mbox{P}_{{\mbox{\scriptsize I}}}$ see Holmes and Spence (1984) and Noonburg (1995). For numerical studies of $\mbox{P}_{{\mbox{\scriptsize II}}}$ see Kashevarov (1998, 2004), Miles (1978, 1980), and Rosales (1978). For numerical studies of $\mbox{P}_{{\mbox{\scriptsize IV}}}$ see Bassom et al. (1993).