An efficient numerical treatment for the asymptotic behaviour of the nonlinear Airy-type problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:375

Article

Seydaoglu, Muaz¹  Kocak, Huseyin²  Erdogan, Utku³ 

[1] Mus Alparslan Univ, Fac Art & Sci, Dept Math, TR-49100 Mus, Turkey

[2] Pamukkale Univ, Quantitat Methods Div, TR-20160 Denizli, Turkey

[3] Eskisehir Tech Univ, Dept Math, TR-26555 Eskisehir, Turkey

关键词: Nonlinear Airy-type equations;    The second Painleve equation;    Symplectic integrator;    Splitting methods;    Magnus expansion;   

DOI  :  10.1016/j.cam.2020.112833

来源: Elsevier

【 摘 要 】

This study focuses on symplectic integrators for numerical evaluation of the asymptotic solutions of the nonlinear Airy-type equations obtained by reducing the nonlinear dispersive equations. Since the nature of Airy-type equations has both highly oscillatory slow decay and exponential fast decay, most of classical integrators are not able to correctly exhibit challenging physical behaviour. We use specially designed symplectic integrators combining splitting methods with Magnus integrators to catch asymptotic behaviour of nonlinear Airy-type equations efficiently, even for large step sizes. Efficiency of the proposed methods for given problems is discussed. Moreover, numerical results obtained by the proposed methods are compared with the existing results in the literature. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free