Solving partial differential equations with point collocation and one-dimensional integrated interpolation schemes

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.

Abstract

[Summary]: This lecture presents an overview of the Integral Collocation formulation for numerically solving partial differential equations (PDEs). However, due to space limitation, the paper only describes the latest development, namely schemes based only on one-dimensional (1D) integrated interpolation even in multi-dimensional problems. The proposed technique is examined with Chebyshev polynomials and radial basis functions (RBFs). The latter can be used in both regular and irregular domains. For both basis functions, the accuracy and convergence rates of the new technique are better than those of the differential formulation.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Lecture)
Refereed: Yes
Item Status: Live Archive
Additional Information: Awaiting copyright advice.
Depositing User: Prof Thanh Tran-Cong
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 07 Feb 2008 23:37
Last Modified: 02 Jul 2013 22:54
Uncontrolled Keywords: partial differential equations, point collocation, integral collocation formulation, one-dimensional integrated interpolation
Fields of Research (FOR2008): 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
URI: http://eprints.usq.edu.au/id/eprint/3575

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