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- Fields of Research (FOR 2008) (23943)
- 01 Mathematical Sciences (1003)
- 0101 Pure Mathematics (175)
**010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems**(40)

- 0101 Pure Mathematics (175)

- 01 Mathematical Sciences (1003)

Number of items at this level: **40**.

Ermakov, A. M. and Stepanyants, Y. A. ORCID: https://orcid.org/0000-0003-4546-0310
(2016)
*Description of vortical flows of incompressible fluid in terms of quasi-potential function.*
In: 20th Australasian Fluid Mechanics Conference (AFMC 2016), 5-8 Dec 2016, Perth, Australia.

Mohammed Al-Badri, Mayada G.
(2015)
*Dynamics of active systems with nonlinear excitation of the phase.*
[Thesis (PhD/Research)]

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.

Giniyatullin, A. R. and Kurkin, A. A. and Kurkina, O. E. and Stepanyants, Y. A. ORCID: https://orcid.org/0000-0003-4546-0310
(2014)
*Generalized Korteweg–de Vries equation for internal waves in two-layer fluid.*
Fundamental and Applied Hydrophysics, 7 (4).
pp. 16-28.
ISSN 2073-6673

Strunin, Dimitry and Mohammed, Mayada
(2013)
*Validity and dynamics in the nonlinearly excited 6th-order phase equation.*
In: 9th American Institute of Mathematical Sciences International Conference on Dynamical Systems, Differential Equations and Applications (AIMS 2013), 1-5 Jul 2012, Orlando, FL. United States.

Strunin, D. V. and Mohammed, M. G.
(2012)
*Parametric space for nonlinearly excited phase equation.*
Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 53 (S).
C236-C248.
ISSN 1446-8735

Strunin, D. V. and Mohammed, F. J.
(2012)
*Numerical analysis of an averaged model of turbulent transport near a roughness layer.*
Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 53 (S).
C142-C154.
ISSN 1446-8735

Roberts, A. J. and MacKenzie, Tony and Bunder, J. E.
(2012)
*Accurate macroscale modelling of spatial dynamics in multiple dimensions.*
Technical Report.
University of Adelaide
, Adelaide, Australia.
[Report]

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T.
(2012)
*Several compact local stencils based on integrated RBFs for fourth-order ODEs and PDEs.*
CMES: Computer Modeling in Engineering and Sciences, 84 (2).
pp. 171-203.
ISSN 1526-1492

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T.
(2011)
*Compact local stencils employed with integrated RBFs for fourth-order differential problems.*
Structural Longevity, 6 (2).
pp. 93-107.
ISSN 1944-611X

Zeiler, Irmgard and Langlands, Trevor and Murray, John M. and Ritter, Alison
(2010)
*Optimal targeting of hepatitis C virus treatment among injecting drug users to those not enrolled in methadone maintenance programs.*
Drug and Alcohol Dependence, 110 (3).
pp. 228-233.
ISSN 0376-8716

Langlands, Trevor and Henry, Bruce and Straka, Peter
(2010)
*Fractional diffusion in force fields, fractional electro-diffusion and fractional chemotaxis diffusion.*
In: Dynamics Days Asia Pacific 6 Conference (DDAP6), 12-14 Jul 2010, Sydney, Australia.

Strunin, D. V.
(2009)
*Phase equation with nonlinear excitation for nonlocally coupled oscillators.*
Physica D: Nonlinear Phenomena, 238 (18).
pp. 1909-1916.
ISSN 0167-2789

Mai-Duy, Nam and Tran-Cong, Thanh
(2009)
*An integrated-RBF technique based on Galerkin formulation for elliptic differential equations.*
Engineering Analysis with Boundary Elements, 33 (2).
pp. 191-199.
ISSN 0955-7997

Roberts, A. J.
(2008)
*Computer algebra derives discretisations via self-adjoint multiscale modelling.*
Unpublished.

Roberts, A. J.
(2008)
*Computer algebra describes flow of turbulent floods via the Smagorinski large eddy closure.*
Technical Report.
University of Southern Queensland
, Toowoomba, Australia.
[Report]

Roberts, A. J.
(2008)
*The inertial dynamics of thin film flow of non-Newtonian fluids.*
Physics Letters Section A: General, Atomic and Solid State Physics, 372 (10).
pp. 1607-1611.
ISSN 0375-9601

Suslov, S. A.
(2008)
*Two-equation model of mean flow resonances in subcritical flow systems.*
Discrete and Continuous Dynamical Systems Series S, Selected Topics, 1 (1).
pp. 165-176.
ISSN 1937-1632

Roberts, A. J.
(2008)
*Normal form transforms separate slow and fast modes in stochastic dynamical systems.*
Physica A: Statistical Mechanics and Its Applications, 387 (1).
pp. 12-38.
ISSN 0378-4371

Stepanyants, Yury A. ORCID: https://orcid.org/0000-0003-4546-0310
(2008)
*Solutions classification to the extended reduced Ostrovsky equation.*
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 4.

Roberts, A. J.
(2007)
*Computer algebra models dynamics on a multigrid across multiple length and time scales.*
Technical Report.
UNSPECIFIED
.
[Report]

Georgiev, D. J. and Roberts, A. J. and Strunin, D. V.
(2007)
*The dynamics of the vertical structure of turbulence in flood flows.*
Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 48 (CTAC-2).
C573-C590.
ISSN 1446-1811

Georgiev, Dian J. and Roberts, A. J. and Strunin, Dmitry V.
(2007)
*Nonlinear dynamics on centre manifolds describing turbulent floods: k-\omega model.*
Discrete and Continuous Dynamical Systems Series A, 2007 (Specia).
pp. 419-428.
ISSN 1078-0947

Roberts, A. J.
(2007)
*Computer algebra models the inertial dynamics of a thin film flow of power law fluids and other non-Newtonian fluids.*
Technical Report.
University of Southern Queensland
.
[Report]

Apel, John R. and Ostrovsky, Lev A. and Stepanyants, Yury A. ORCID: https://orcid.org/0000-0003-4546-0310 and Lynch, James F.
(2007)
*Internal solitons in the ocean and their effect on underwater sound.*
Journal of the Acoustical Society of America, 121 (2).
pp. 695-722.
ISSN 0001-4966

Roberts, A. J.
(2007)
*Computer algebra derives normal forms of stochastic differential equations.*
Technical Report.
University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing
, Toowoomba, Australia.
[Report]

Li, Zhenquan and Roberts, A. J.
(2007)
*A flexible error estimate for the application of centre manifold theory.*
Global Journal of Pure and Applied Mathematics, 3 (3).
pp. 241-249.
ISSN 0973-1768

Roberts, A. J. and Kevrekidis, I. G.
(2007)
*General tooth boundary conditions for equation free modeling.*
SIAM Journal on Scientific Computing, 29 (4).
pp. 1495-1510.
ISSN 1064-8275

Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I.
(2006)
*A new high-order time-kernel BIEM for the Burgers equation.*
CMES: Computer Modeling in Engineering and Sciences, 16 (3).
pp. 177-186.
ISSN 1526-1492

Roberts, A. J.
(2006)
*Resolving the multitude of microscale interactions accurately models stochastic partial differential equations.*
LMS Journal of Computation and Mathematics, 9.
pp. 193-221.

Roberts, A. J.
(2006)
*Computer algebra derives discretisations of the stochastically forced Burgers' partial differential equation.*
Technical Report.
University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing
, Toowoomba, Australia.
[Report]

Roberts, A. J.
(2006)
*Resolve the multitude of microscale interactions to holistically discretise the stochastically forced Burgers' partial differential equation.*
Technical Report.
University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing
, Toowoomba, Australia.
[Report]

MacKenzie, T. and Roberts, A. J.
(2006)
*Accurately model the Kuramoto-Sivashinsky dynamics with holistic discretisation.*
SIAM Journal on Applied Dynamical Systems, 5 (3).
pp. 365-402.

Roberts, A. J.
(2005)
*Computer algebra resolves a multitude of microscale interactions to model stochastic partial differential equations.*
Technical Report.
University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing
, Toowoomba, Australia.
[Report]

Mai-Duy, N. and Tanner, R. I.
(2005)
*Computing non-Newtonian fluid flow with radial basis function networks.*
International Journal for Numerical Methods in Fluids, 48 (12).
pp. 1309-1336.
ISSN 0271-2091

Mai-Duy, Nam
(2005)
*Solving high order ordinary differential equations with radial basis function networks.*
International Journal for Numerical Methods in Engineering, 62 (6).
pp. 824-852.
ISSN 0029-5981

Roberts, A. J.
(2003)
*A holistic finite difference approach models linear dynamics consistently.*
Mathematics of Computation, 72 (241).
pp. 247-262.
ISSN 0025-5718

Mei, Z. and Roberts, A. J. and Li, Zhenquan
(2002)
*Modelling the dynamics of turbulent floods.*
SIAM Journal on Applied Mathematics, 63 (2).
pp. 423-458.
ISSN 0036-1399

Melnik, R. V. N. and Roberts, A. J. and Thomas, K. A.
(2001)
*Coupled thermomechanical dynamics of phase transitions in shape memory alloys and related hysteresis phenomena.*
Mechanics Research Communications, 28 (6).
pp. 637-651.
ISSN 0093-6413

Mai-Duy, Nam and Tran-Cong, Thanh
(2001)
*Numerical solution of differential equations using multiquadric radial basis function networks.*
Neural Networks, 14 (2).
pp. 185-199.
ISSN 0893-6080