期刊
APPLIED MATHEMATICS AND COMPUTATION
卷 218, 期 9, 页码 4684-4694出版社
ELSEVIER SCIENCE INC
DOI: 10.1016/j.amc.2011.11.005
关键词
Numerical continuation; Periodic travelling wave; Wave train; Auto; Partial differential equations
资金
- Leverhulme Trust
Periodic travelling waves (wavetrains) are an important solution type for many partial differential equations. In this paper I review the use of numerical continuation for studying these solutions. I discuss the calculation of the form and stability of a given periodic travelling wave, and the calculation of boundaries in a two-dimensional parameter plane for wave existence and stability. I also describe the automated implementation of these numerical continuation procedures via the software package WAVETRAIN (http://www.ma.hw.ac.uk/wavetrain). I conclude by discussing ongoing work on numerical continuation methods for determining the absolute stability of periodic travelling waves. (C) 2011 Elsevier Inc. All rights reserved.
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