32 Painlevé Transcendents Computation 32.16 Physical 33 Coulomb Functions

§32.17 Methods of Computation

Keywords:: Painlevé transcendents
Referenced by:: Other Changes
Permalink:: http://dlmf.nist.gov/32.17
Addition (effective with 1.0.5):: The reference to Olver (2011) has been added in this section.
Reported 2012-09-19

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 $\mbox{P}_{{\mbox{\scriptsize I}}}$ see Holmes and Spence (1984), Noonburg (1995), and Fornberg and Weideman (2011). For numerical studies of $\mbox{P}_{{\mbox{\scriptsize II}}}$ see Rosales (1978), Miles (1978, 1980), Kashevarov (1998, 2004), and S. Olver (2011). For numerical studies of $\mbox{P}_{{\mbox{\scriptsize IV}}}$ see Bassom et al. (1993).