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- Fields of Research (FOR 2008) (13679)
- 01 Mathematical Sciences (692)
- 0103 Numerical and Computational Mathematics (203)
**010302 Numerical Solution of Differential and Integral Equations**(83)

- 0103 Numerical and Computational Mathematics (203)

- 01 Mathematical Sciences (692)

Number of items at this level: **83**.

Nikitenkova, S. P. and Raj, N. and Stepanyants, Y. A.
(2015)
*Nonlinear vector waves of a flexural mode in a chain model of atomic particles.*
Communications in Nonlinear Science and Numerical Simulation, 20 (3).
pp. 731-742.
ISSN 1007-5704

An-Vo, D. - A. and Mai-Duy, N. and Tran, C. - D. and Tran-Cong, T.
(2013)
*ADI method based on C2-continuous two-node integrated-RBF elements for viscous flows.*
Applied Mathematical Modelling, 37 (7).
pp. 5184-5203.
ISSN 0307-904X

Mai-Duy, N. and Tran-Cong, T.
(2013)
*A compact five-point stencil based on integrated RBFs for 2D second-order differential problems.*
Journal of Computational Physics, 235.
pp. 302-321.
ISSN 0021-9991

Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2013)
*A direct forcing immersed boundary method employed with compact integrated RBF approximations for heat transfer and fluid flow problems.*
CMES Computer Modeling in Engineering and Sciences, 96 (1).
pp. 49-90.
ISSN 1526-1492

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2013)
*A finite-volume method based on compact local integrated radial basis function approximations for second-order differential problems.*
CMES Computer Modeling in Engineering and Sciences, 91 (6).
pp. 485-516.
ISSN 1526-1492

Pham-Sy, N. and Tran, C.-D. and Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran-Cong, T.
(2013)
*Compact local IRBF and domain decomposition method for solving PDEs using a distributed termination detection based parallel algorithm.*
CMES Computer Modeling in Engineering and Sciences, 92 (1).
pp. 1-31.
ISSN 1526-1492

Thai-Quang, N. and Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2012)
*A high-order compact integrated-RBF scheme for time-dependent problems.*
In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

Mai-Cao, L. and Tran-Cong, T.
(2012)
*A new IRBFN scheme for the numerical simulation of interfacial flows.*
In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

Hoang-Trieu, T.-T. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2012)
*Compact local integrated RBF stencil based on finite volume formulation for second-order differential problems.*
In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

Pham-Sy, N. and Hoang-Trieu, T.-T. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T.
(2012)
*Development of parallel algorithm for boundary value problems using compact local integrated RBFN and domain decomposition.*
In: 4th International Conference on Computational Methods (ICCM 2012), 25-28 Nov 2012, Gold Coast, Australia.

Tran, Canh-Dung and Mai-Duy, Nam and Tran-Cong, Thanh
(2012)
*Computation of a Fokker-Planck-equation-based multi-scale model for complex flows using the IRBFN method.*
In: 6th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), 10-14 Sep 2012, Vienna, Austria.

Tran, C. -D. and Mai-Duy, N. and Tran-Cong, T.
(2012)
*Numerical solution of Fokker-Planck equation using the integral radial basis function networks.*
In: 10th World Congress on Computational Mechanics (WCCM 2012), 8-13 Jul 2012, Sao Paulo, Brazil.

Ma, Xing and Mills, Julie E. and Brown, Graham and Zhuge, Yan
(2012)
*A force method model for static analysis of transmission line system subjected to in-plane and out-of-plane loadings.*
Advanced Materials Research, 368-37.
pp. 3535-3538.
ISSN 1662-8985

Obregon, M. A. and Stepanyants, Y. A.
(2012)
*On numerical solution of the Gardner Ostrovsky equation.*
Mathematical Modelling of Natural Phenomena, 7 (2).
pp. 113-130.
ISSN 0973-5348

Tran, C.-D. and Mai-Duy, N. and Le-Cao, K. and Tran-Cong, T.
(2012)
*A continuum-microscopic method based on IRBFs and control volume scheme for viscoelastic fluid flows.*
CMES: Computer Modeling in Engineering and Sciences, 85 (6).
pp. 499-519.
ISSN 1526-1492

Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T.
(2012)
*A numerical procedure based on 1D-IRBFN and local MLS-1D-IRBFN methods for fluid-structure interaction analysis.*
CMES: Computer Modeling in Engineering and Sciences, 83 (5).
pp. 459-498.
ISSN 1526-1492

Thai-Quang, N. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2012)
*High-order alternating direction implicit method based on compact integrated-RBF approximations for unsteady/steady convection-diffusion equations.*
CMES: Computer Modeling in Engineering and Sciences, 89 (3).
pp. 189-220.
ISSN 1526-1492

Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T.
(2012)
*Local moving least square - one-dimensional IRBFN technique: part 11 - unsteady incompressible viscous flows.*
CMES: Computer Modeling in Engineering and Sciences , 83 (3).
pp. 311-351.
ISSN 1526-1492

An-Vo, D.-A. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2012)
*Modeling strain localisation in a segmented bar by a C2-continuous two-node integrated-RBF element formulation.*
In: 34th International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2012), 25-27 Jun 2012, Split, Croatia.

An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T.
(2012)
*RBF computation of multiscale elliptic problems [Keynote paper].*
In: 8th ICCES Special Symposium on Meshless & Other Novel Computational Methods (ICCES MM 2012), 2-6 Sep 2012, Budva, Montenegro.

An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T.
(2012)
*RBF-based multiscale control volume method for second order elliptic problems with oscillatory coefficients.*
CMES: Computer Modeling in Engineering and Sciences, 89 (4).
pp. 303-359.
ISSN 1526-1492

Yevdokimov, Oleksiy
(2011)
*Problem set 8.*
Australian Senior Mathematics Journal, 25 (2).
p. 63.
ISSN 0819-4564

Mai-Duy, N. and Tran-Cong, T.
(2011)
*Compact local integrated-RBF approximations for second-order elliptic differential problems.*
Journal of Computational Physics , 230 (12).
pp. 4772-4794.
ISSN 0021-9991

Yevdokimov, Oleksiy
(2011)
*Problem set 7.*
Australian Senior Mathematics Journal, 25 (1).
p. 64.
ISSN 0819-4564

Waite, I. A. and Marsden, S. C. and Carter, B. D. and Hart, R. and Donati, J. -F. and Ramirez Velez, J. C. and Semel, M. and Dunstone, N.
(2011)
*Magnetic fields and differential rotation on the pre-main sequence - III. The early-G star HD 106506.*
Monthly Notices of the Royal Astronomical Society, 413 (3).
pp. 1949-1960.
ISSN 0035-8711

Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2011)
*Numerical study of stream-function formulation governing flows in multiply-connected domains by integrated RBFs and Cartesian grids.*
Computers and Fluids , 44 (1).
pp. 32-42.
ISSN 0045-7930

Nguyen-Van, H. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T.
(2011)
*Buckling and vibration analysis of laminated composite plate/shell structures via a smoothed quadrilateral flat shell element with in-plane rotations.*
Computers and Structures, 89 (7-8).
pp. 612-625.
ISSN 0045-7949

Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T.
(2011)
*Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method.*
Computers and Structures, 89 (1-2).
pp. 1-13.
ISSN 0045-7949

An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T.
(2011)
*A C2-continuous control-volume technique based on cartesian grids and two-node integrated-RBF elements for second-order elliptic problems.*
CMES: Computer Modeling in Engineering and Sciences, 72 (4).
pp. 299-334.
ISSN 1526-1492

Mai-Duy, N. and Tran-Cong, T. and Phan-Thien, N.
(2011)
*A numerical technique based on integrated RBFs for the system evolution in molecular dynamics.*
CMES: Computer Modeling in Engineering and Sciences, 79 (4).
pp. 223-236.
ISSN 1526-1492

Mai-Duy, N. and Tran-Cong, T.
(2011)
*A stable and accurate control-volume technique based on integrated radial basis function networks for fluid-flow problems.*
In: ACAM 6: 6th Australasian Congress on Applied Mechanics , 12-15 Dec 2010, Perth, Western Australia.

Mai-Duy, Nam and Tran-Cong, Thanh
(2011)
*Compact local approximations employed with integrated RBFs for second-order elliptic differential equations.*
In: 3rd International Symposium on Computational Mechanics (ISCM III) and 2nd Symposium on Computational Structural Engineering (CSE II), 5-7 Dec 2011, Taipei, Taiwan.

An-Vo, D. A. and Mai-Duy, N. and Tran-Cong, T.
(2011)
*High-order upwind methods based on C2-continuous two-node integrated-RBF elements for viscous flows.*
CMES: Computer Modeling in Engineering and Sciences, 80 (2).
pp. 141-177.
ISSN 1526-1492

An-Vo, D.-A. and Tran, C.-D. and Mai-Duy, N. and Tran-Cong, T.
(2011)
*IRBFN-based multiscale solution of a model 1D elliptic equation.*
In: 33rd International Conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM 2011), 28-30 Jun 2011, New Forest, United Kingdom.

Ngo-Cong, D. and Mai-Duy, N. and Karunasena, W. and Tran-Cong, T.
(2011)
*Moving least square - one dimensional integrated radial basis function networks for time dependent problems.*
In: 33rd International Conference on Boundary Elements and other Mesh Reduction Methods, 28-30 Jun 2011, New Forest, UK.

Ho-Minh, D. and Le-Cao, K. and Mai-Duy, N. and Tran-Cong, T.
(2010)
*Simulation of fluid flows at high Reynolds/Rayleigh numbers using integrated radial basis functions.*
In: 17th Australasian Fluid Mechanics Conference (AFMC 2010), 5-9 Dec 2010, Auckland, New Zealand.

Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*A numerical study of 2D integrated RBFNs incorporating Cartesian grids for solving 2D elliptic differential problems.*
Numerical Methods for Partial Differential Equations, 26 (6).
pp. 1443-1462.
ISSN 0749-159X

Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*Point-wise integrated-RBF-based discretisation of differential equations.*
In: 2nd International Symposium on Computational Mechanics (ISCM II) in conjunction with EPMESC 2009, 30 Nov-3 Dec 2009, Hong Kong, Macau.

Ghabraie, Kazem and Xie, Yi Min and Huang, Xiaodong and Ren, Gang
(2010)
*Shape and reinforcement optimization of underground tunnels.*
Journal of Computational Science and Technology, 4 (1).
pp. 51-63.

Le, Phong B. H. and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham
(2010)
*A cartesian-grid collocation technique with integrated radial basis functions for mixed boundary value problems.*
International Journal for Numerical Methods in Engineering, 82 (4).
pp. 435-463.
ISSN 0029-5981

Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*A control volume technique based on integrated RBFNs for the convection-diffusion equation.*
Numerical Methods for Partial Differential Equations, 26 (2).
426 -447.
ISSN 0749-159X

Le, Phong
(2010)
*RBF-based meshless modeling of strain localization and fracture.*
[Thesis (PhD/Research)]
(Unpublished)

Ho-Minh, D. and Mai-Duy, N. and Tran-Cong, T.
(2010)
*A Cartesian-grid integrated-RBF Galerkin technique.*
In:
Recent studies in meshless and other novel computational methods.
Tech Science Press, Duluth, GA. USA, pp. 87-102.
ISBN 978-0-9824205-4-6

Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*A moving IRBFN-based Galerkin meshless method.*
CMES: Computer Modeling in Engineering and Sciences, 66 (1).
pp. 25-52.
ISSN 1526-1492

Le, Phong B. H. and Rabczuk, Timon and Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*A moving IRBFN-based integration-free meshless method.*
CMES: Computer Modeling in Engineering and Sciences, 61 (1).
pp. 63-109.
ISSN 1526-1492

Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*A simple and effective preconditioner for integrated-RBF-based Cartesian-grid schemes.*
In: 2010 International Conference on Computational and Experimental Engineering & Sciences 2010, 28 Mar - 1 Apr 2010, Las Vegas, USA.

Ho-Minh, D. and Mai-Duy, Nam and Tran-Cong, Thanh
(2010)
*Galerkin/collocation methods based on 1D-integrated-RBFNs for viscoelastic flows.*
CMES: Computer Modeling in Engineering and Sciences, 70 (3).
pp. 217-251.
ISSN 1526-1492

Le-Cao, K. and Mai-Duy, N. and Tran, C.-D. and Tran-Cong, T.
(2010)
*Towards an analysis of shear suspension flows using radial basis functions.*
CMES: Computer Modeling in Engineering and Sciences, 67 (3).
pp. 265-294.
ISSN 1526-1492

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

Mai-Duy, Nam and Tran-Cong, Thanh
(2009)
*A Cartesian-grid discretisation scheme based on local integrated RBFNs for two-dimensional elliptic problems.*
CMES: Computer Modeling in Engineering and Sciences, 51 (3).
pp. 213-238.
ISSN 1526-1492

Mai-Duy, Nam and Tran-Cong, Thanh
(2008)
*A second-order continuity domain-decomposition technique based on integrated Chebyshev polynomials for two-dimensional elliptic problems.*
Applied Mathematical Modelling, 32 (12).
pp. 2851-2862.
ISSN 0307-904X

Mai-Duy, Nam and See, Howard and Tran-Cong, Thanh
(2008)
*An integral-collocation-based fictitious-domain technique for solving elliptic problems.*
Communications in Numerical Methods in Engineering, 24 (11).
pp. 1291-1314.
ISSN 1069-8299

Mai-Duy, Nam and Tran-Cong, Thanh
(2008)
*An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equations.*
Communications in Numerical Methods in Engineering, 24 (10).
pp. 795-806.
ISSN 1069-8299

Mai-Duy, Nam and Tran-Cong, Thanh
(2008)
*A multidomain integrated-radial-basis-function collocation method for elliptic problems.*
Numerical Methods for Partial Differential Equations, 24 (5).
pp. 1301-1320.
ISSN 0749-159X

Mai-Duy, N. and Tran-Cong, T.
(2008)
*A point-collocation method based on integrated Chebyshev polynomials for elliptic differential equations in irregular domains.*
In: 8th World Congress on Computational Mechanics (WCCM8), 30 Jun-4 Jul 2008, Venice, Italy.

Yevdokimov, Oleksiy
(2008)
*Problem set 2.*
Australian Senior Mathematics Journal, 22 (2).
pp. 63-64.
ISSN 0819-4564

Mai-Duy, N. and Tran-Cong, T.
(2008)
*A meshless technique based on integrated radial basis function networks for elliptic partial differential equations.*
In: 4th International Workshop on Meshfree Methods for Partial Differential Equations, 17-20 Sep 2007, Bonn, Germany.

Mai-Duy, Nam and Tran-Cong, Thanh
(2008)
*A multidomain integrated RBF collocation method for elliptic differential equations.*
In: 8th World Congress on Computational Mechanics (WCCM8), and 5th European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2008), 30 June - 4 July 2008, Venice, Italy.

Mai-Duy, N. and Tran-Cong, T.
(2008)
*An effective high-order point-collocation numerical approach based on integrated approximants for elliptic differential equations.*
In:
Leading-edge applied mathematical modeling research.
Nova Science Publishers, Inc., New York, NY. United States, pp. 215-250.
ISBN 978-1-60021-977-1

Mai-Duy, Nam and Tran-Cong, Thanh
(2008)
*On the use of integrated RBFs in Galerkin approximation for elliptic problems.*
In: BEM/MRM 30: 30th International Conference on Boundary Elements and Other Mesh Reduction Methods, 7-9 Jul 2008, Maribor, Slovenia.

Mai-Duy, Nam and Tran-Cong, Thanh
(2007)
*Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes.*
In: 14th International Conference on Computational & Experimental Engineering and Sciences, 1-3 Jan 2007, Miami, Florida, USA.

Mai-Duy, Nam and Tran-Cong, Thanh
(2007)
*A Cartesian-grid collocation method based on radial-basis-function networks for solving PDEs in irregular domains.*
Numerical Methods for Partial Differential Equations, 23 (5).
pp. 1192-1210.
ISSN 0749-159X

Mai-Duy, Nam and Tanner, Roger I.
(2007)
*A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems.*
Journal of Computational and Applied Mathematics, 201 (1).
pp. 30-47.
ISSN 0377-0427

Mai-Duy, Nam and Mai-Cao, Lan and Tran-Cong, Thanh
(2007)
*Computation of transient viscous flows using indirect radial basis function networks.*
CMES: Computer Modeling in Engineering and Sciences, 18 (1).
pp. 59-78.
ISSN 1526-1492

Mai-Duy, N. and Tanner, R. I.
(2007)
*A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs.*
International Journal of Numerical Methods for Heat and Fluid Flow, 17 (2).
pp. 165-186.
ISSN 0961-5539

Le, Phong and Mai-Duy, Nam and Tran-Cong, Thanh and Baker, Graham
(2007)
*A numerical study of strain localization in elasto-thermo-viscoplastic materials using radial basis function networks.*
Computers, Materials and Continua, 5 (2).
pp. 129-150.
ISSN 1546-2218

Nguyen-Van, Hieu and Mai-Duy, Nam and Tran-Cong, Thanh
(2007)
*A simple and accurate four-node quadrilateral element using stabilized nodal integration for laminated plates.*
CMC: Computers, Materials and Continua, 6 (3).
pp. 159-176.
ISSN 1546-2218

Mai-Duy, N. and Tran-Cong, T. and Tanner, R. I.
(2006)
*A domain-type boundary-integral-equation method for two-dimensional biharmonic Dirichlet problem.*
Engineering Analysis with Boundary Elements, 30 (10).
pp. 809-817.
ISSN 0955-7997

Mai-Duy, Nam
(2006)
*An effective spectral collocation method for the direct solution of high-order ODEs.*
Communications in Numerical Methods in Engineering, 22 (6).
pp. 627-642.
ISSN 1069-8299

Mai-Duy, Nam and Tran-Cong, Thanh and Tanner, R. I.
(2006)
*A high-order time-kernel BIEM for the Burgers equation.*
In: International Conference on Boundary Element Techniques VII, 4-6 September 2006, Paris, France.

Roberts, A. J. and Kevrekidis, I. G.
(2005)
*Higher order accuracy in the gap-tooth scheme for large-scale dynamics using microscopic simulators.*
In: CTAC 2004: 12th Biennial Computational Techniques and Applications Conference, Sep 2004, Melbourne, Australia.

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

Mai-Cao, L. and Tran-Cong, T.
(2005)
*A meshless IRBFN-based method for transient problems.*
CMES: Computer Modeling in Engineering and Sciences, 7 (2).
pp. 149-171.
ISSN 1526-1492

Strunin, Dmitry V.
(2005)
*Attractors and centre manifolds in nonlinear diffusion.*
In: 2nd International Conference on Scientific Computing and Partial Differential Equations & The First East Asian SIAM Symposium, 12-16 Dec 2005, Hong Kong.

Tran, Canh-Dung and Tran-Cong, Thanh
(2004)
*Element-free simulation of dilute polymeric flows using Brownian configuration fields.*
Korea-Australia Rheology Journal, 16 (1).
pp. 1-15.
ISSN 1226-119X

Ujevic, Nenad and Roberts, A. J.
(2004)
*A corrected quadrature formula and applications.*
ANZIAM Journal (Australian & New Zealand Industrial and Applied Mathematics Journal), 45 (E).
E41-E56.
ISSN 1446-1811

Passmore, Tim and Roberts, A. J.
(2003)
*Low Prandtl number fluid convection modelled using symbolic algebra (REDUCE) and Matlab.*
In: ANZIAM 2003: Computational Techniques and Applications, 16-18 Jul 2003, Toowoomba, Australia.

Mai-Duy, N. and Tran-Cong, T.
(2003)
*Indirect RBFN method with thin plate splines for numerical solution of differential equations.*
CMES Computer Modeling in Engineering and Sciences, 4 (1).
pp. 85-102.
ISSN 1526-1492

Melnik, Roderick V. N. and Roberts, A. J.
(2003)
*Modelling nonlinear dynamics of shape-memory-alloys with approximate models of coupled thermoelasticity.*
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, 83 (2).
pp. 93-104.
ISSN 0044-2267

Mai-Duy, Nam and Tran-Cong, Thanh
(2003)
*RBF interpolation of boundary values in the BEM for heat transfer problems.*
International Journal of Numerical Methods for Heat and Fluid Flow, 13 (5/6).
pp. 611-632.
ISSN 0961-5539

Tran, Canh-D. and Tran-Cong, T.
(2002)
*BEM-NN computation of generalised Newtonian flows.*
Engineering Analysis with Boundary Elements, 26 (1).
pp. 15-28.
ISSN 0955-7997

Tran, Canh-Dung and Tran-Cong, Thanh
(2002)
*Computation of viscoelastic flow using neural networks and stochastic simulation.*
Korea-Australia Rheology Journal, 14 (4).
pp. 161-174.
ISSN 1226-119X

Mai-Duy, Nam and Tran-Cong, Thanh
(2001)
*Numerical solution of Navier-Stokes equations using multiquadric radial basis function networks.*
International Journal for Numerical Methods in Fluids, 37 (1).
pp. 65-86.
ISSN 0271-2091