A Computational Exploration of the Second Painlevé Equation
نویسندگان
چکیده
The pole field solver developed recently by the authors (J. Comp. Phys., 230 (2011), 5957–5973) is used to survey the space of solutions of the second Painlevé equation that are real on the real axis. This includes well-known solutions such as the Hastings-McLeod and Ablowitz-Segur type of solutions, as well as some novel solutions. The speed and robustness of this pole field solver enable the exploration of pole dynamics in the complex plane as the parameter and initial conditions of the differential equation are varied. Theoretical connection formulas are also verified numerically.
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ورودعنوان ژورنال:
- Foundations of Computational Mathematics
دوره 14 شماره
صفحات -
تاریخ انتشار 2014