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Numerical study of the asymptotics of the second Painlevé equation by a functional fitting method
Author(s) -
Erdoğan Utku,
Koçak Huseyin
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2757
Subject(s) - mathematics , integrator , nonlinear system , oscillation (cell signaling) , numerical analysis , korteweg–de vries equation , mathematical analysis , soliton , runge–kutta methods , order (exchange) , physics , quantum mechanics , genetics , finance , voltage , economics , biology
The Painlevé equations arise as reductions of the soliton equations such as the Korteweg–de Vries equation, the nonlinear Schrödinger equation and so on. In this study, we are concerned with numerical approximation of the asymptotics of solutions of the second Painlevé equation on pole‐free intervals along the real axis. Classical integrators such as high order Runge–Kutta schemes might be expensive to simulate oscillation, decay and blow‐up behaviours depending on initial conditions. However, a lower order functional fitting method catches all kinds of solutions even for relatively large step sizes. Copyright © 2013 John Wiley & Sons, Ltd.