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

Mohammed, Mayada and Strunin, Dmitry (2014) Finite-difference approach for a 6th-order nonlinear phase equation with self-excitation. In: 12th Asia Pacific Physics Conference 2013, 14-19 Jul 2013, Makuhari, Japan.

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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.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: © 2014 The Physical Society of Japan. Permanent restricted access to published version due to publisher copyright policy.
Faculty / Department / School: Current - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences
Date Deposited: 05 May 2015 00:58
Last Modified: 25 May 2017 00:23
Uncontrolled Keywords: nonlinear partial differential equation; finite difference; self-excitation
Fields of Research : 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970102 Expanding Knowledge in the Physical Sciences
E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/24910

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