Compact local stencils employed with integrated RBFs for fourth-order differential problems

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

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Abstract

In this paper, new compact local stencils based on integrated radial basis functions (IRBFs) for solving fourth-order ordinary differential equations (ODEs) and partial differential equations (PDEs) are presented. The integration constants arising from the construction of IRBFs are exploited to incorporate into the local IRBF approximations values of the ODEs/PDEs at selected nodal points. The proposed stencils, which lead to sparse system matrices, are numerically validated through the solution of several analytic test problems. Numerical results indicate that their solutions converge very fast with grid refinement.

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Item Type:	Article (Commonwealth Reporting Category C)
Refereed:	No
Item Status:	Live Archive
Additional Information:	Tech Science Press © 2011.
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013)
Faculty/School / Institute/Centre:	Historic - Faculty of Engineering and Surveying - No Department (Up to 30 Jun 2013)
Date Deposited:	18 Jun 2013 04:23
Last Modified:	30 Jan 2017 01:29
Uncontrolled Keywords:	compact local approximations; high-order ODEs; high-order PDEs; integrated radial basis functions
Fields of Research (2008):	01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems 01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods 09 Engineering > 0999 Other Engineering > 099999 Engineering not elsewhere classified
Fields of Research (2020):	49 MATHEMATICAL SCIENCES > 4904 Pure mathematics > 490409 Ordinary differential equations, difference equations and dynamical systems 49 MATHEMATICAL SCIENCES > 4901 Applied mathematics > 490101 Approximation theory and asymptotic methods 40 ENGINEERING > 4099 Other engineering > 409999 Other engineering not elsewhere classified
Socio-Economic Objectives (2008):	E Expanding Knowledge > 97 Expanding Knowledge > 970109 Expanding Knowledge in Engineering
Identification Number or DOI:	https://doi.org/10.3970/sl.2011.006.093
URI:	http://eprints.usq.edu.au/id/eprint/22675

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