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International Journal of Computer Mathematics Volume 86, 2009 - Issue 10-11: COMPUTATIONAL AND MATHEMATICAL METHODS IN SCIENCE AND ENGINEERING
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Original Articles

A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations

N. Mai-Duy Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD, AustraliaCorrespondence[email protected]
,
D. Ho-Minh Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD, Australia
&
T. Tran-Cong Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying, The University of Southern Queensland, Toowoomba, QLD, Australia
Pages 1746-1759 | Received 07 Sep 2008, Accepted 24 Nov 2008, Published online: 18 Nov 2010

References

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  • de Vahl Davis , G. 1983 . Natural convection of air in a square cavity: a bench mark numerical solution . Int. J. Numer. Methods Fluids , 3 : 249 – 264 .
  • Le Quere , P. 1991 . Accurate solutions to the square thermally driven cavity at high Rayleigh number . Comput. Fluids , 20 : 29 – 41 .
  • Mai-Duy , N. and Tanner , R. I. 2007 . A collocation method based on one-dimensional RBF interpolation scheme for solving PDEs . Int. J. Numer. Methods Heat Fluid Flow , 17 : 165 – 186 .
  • Mai-Duy , N. and Tran-Cong , T. 2001 . Numerical solution of differential equations using multiquadric radial basis function networks . Neural Netw. , 14 : 185 – 199 .
  • Mai-Duy , N. and Tran-Cong , T. 2003 . Approximation of function and its derivatives using radial basis function networks . Appl. Math. Model. , 27 : 197 – 220 .
  • Mai-Duy , N. and Tran-Cong , T. 2007 . A Cartesian-grid collocation method based on radial-basis- function networks for solving PDEs in irregular domains . Numer. Methods Partial Differ. Eq. , 23 : 1192 – 1210 .
  • Mai-Duy , N. and Tran-Cong , T. 2009 . An integrated-RBF technique based on Galerkin formulation for elliptic differential equations . Eng. Anal. Bound. Elements , 33 : 191 – 199 .
  • Zienkiewicz , O. C. and Taylor , R. L. 2000 . The Finite Element Method – Volume 2: Solid Mechanics , Oxford : Butterworth Heinemann .

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