Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation

Paper

Mohammed, Mayada and Strunin, Dmitry. 2014. "Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation." Nagamiya, Shoji and Motobayashi, Tohru (ed.) 12th Asia Pacific Physics Conference 2013. Makuhari, Japan 14 - 19 Jul 2013 Makuhari, Japan.
Paper/Presentation Title

Finite-difference approach for a 6th-order nonlinear phase
equation with self-excitation

Presentation TypePaper
AuthorsMohammed, Mayada (Author) and Strunin, Dmitry (Author)
EditorsNagamiya, Shoji and Motobayashi, Tohru
Journal or Proceedings TitleProceedings of the 12th Asia Pacific Physics Conference (APPC 2013)
Journal Citation1, p. 16003
Number of Pages4
Year2014
Place of PublicationMakuhari, Japan
ISBN9784890271016
Web Address (URL) of Paperhttp://journals.jps.jp/doi/pdf/10.7566/JPSCP.1.016003
Conference/Event12th Asia Pacific Physics Conference 2013
Event Details
12th Asia Pacific Physics Conference 2013
Event Date
14 to end of 19 Jul 2013
Event Location
Makuhari, Japan
Abstract

A range of physical systems, particularly of chemical nature involving reactions, perform self-excited
oscillations coupled by diffusion. The role of diffusion is not trivial so that initial differences in the phase of the oscillations between different points in space do not necessarily disappear as time goes; they may self-sustain. The dynamics of the phase depend on the values of the controlling parameters of the system. We consider a 6th-order nonlinear partial differential equation resulting
in such dynamics. The equation is solved using central finite-difference discretization in space. The resulting system of ordinary differential equations is integrated in time using a Matlab solver. The numerical code is tested using forced versions of the equation, which admit exact analytical solutions. The comparison of the exact and numerical solutions demonstrates satisfactory agreement.

Keywordsnonlinear partial differential equation; finite difference; self-excitation
ANZSRC Field of Research 2020490409. Ordinary differential equations, difference equations and dynamical systems
490105. Dynamical systems in applications
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Byline AffiliationsSchool of Agricultural, Computational and Environmental Sciences
Computational Engineering and Science Research Centre
Institution of OriginUniversity of Southern Queensland
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