Strunin, Dmitry V. and Ngo-Cong, Duc and Bhanot, Rajeev (2015) Using 1D-IRBFN method for solving high-order nonlinear differential equations arising in models of active-dissipative systems. In: 1st Pan-American Congress on Computational Mechanics, (PANACM 2015) in conjunction with the XI Argentine Congress on Computational Mechanics (MECOM 2015), 27-29 April 2015, Buenos Aires, Argentina.
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Abstract
We analyse a nonlinear partial differential equation modelling reaction-diffusion systems with nonlocal coupling and reaction fronts of gasless combustion. The equation is of active-dissipative type, nonlinear, with 6th-order spatial derivative. To numerically solve the equations we use the one-dimensional integrated radial basis function network (1D-IRBFN)method. The method has been previously developed and successfully applied to several problems
such as structural analysis, viscous and viscoelastic flows and fluid-structure interaction. A commonly used approach is to differentiate a function of interest to obtain approximate derivatives. However, this leads to a reduction in convergence rate for derivatives and this reduction is an increasing function of derivative order. Accordingly, differentiation magnifies errors. To avoid this problem and recognising that integration is a smoothing process, the proposed 1D-IRBFN method uses the integral formulation, where spectral approximants are utilised to represent highest-order derivatives under consideration and then integrated analytically to yield approximate expressions for lower-order derivatives and the function itself. Our preliminary results demonstrate good performance of the 1D-IRBFN algorithm for the equation under consideration.
Numerical solutions representing travelling waves are obtained, in agreement with the earlier studies.
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| Item Type: | Conference or Workshop Item (Commonwealth Reporting Category E) (Paper) |
|---|---|
| Refereed: | Yes |
| Item Status: | Live Archive |
| Additional Information: | © The authors. |
| Faculty/School / Institute/Centre: | Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019) |
| Faculty/School / Institute/Centre: | Historic - Faculty of Health, Engineering and Sciences - School of Agricultural, Computational and Environmental Sciences (1 Jul 2013 - 5 Sep 2019) |
| Date Deposited: | 24 Jun 2016 01:40 |
| Last Modified: | 27 Aug 2018 23:02 |
| Uncontrolled Keywords: | 1D-IRBFN numerical method; nonlinear active-dissipative PDE |
| Fields of Research (2008): | 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations 01 Mathematical Sciences > 0102 Applied Mathematics > 010204 Dynamical Systems in Applications |
| Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4903 Numerical and computational mathematics > 490303 Numerical solution of differential and integral equations 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490105 Dynamical systems in applications |
| Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |
| URI: | http://eprints.usq.edu.au/id/eprint/28507 |
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