A high-order compact integrated-RBF scheme for time-dependent problems

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.

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Abstract

This paper presents a high-order approximation scheme based on compact integrated radial basis function (RBF) stencils and second-order Adams-Bashforth/Crank-Nicolson algorithms for solving time-dependent problems. We employ compact integrated-RBF stencils, where the RBF approximations are locally constructed through integration and expressed in terms of nodal values of the function and its derivatives, to discretise the spatial derivatives in the governing equations. We adopt the Adams-Bashforth and Crank-Nicolson algorithms, which are second-order accurate, to discretise the temporal derivatives. Numerical investigations in several analytic test problems show that the proposed scheme is stable and high-order accurate.


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Item Type: Conference or Workshop Item (Commonwealth Reporting Category E) (Paper)
Refereed: Yes
Item Status: Live Archive
Additional Information: No evidence of copyright restrictions preventing deposit.
Faculty / Department / School: Historic - Faculty of Engineering and Surveying - Department of Mechanical and Mechatronic Engineering
Date Deposited: 14 Apr 2013 23:32
Last Modified: 14 Oct 2014 23:53
Uncontrolled Keywords: time-dependent problems; compact integrated-RBF stencils; high-order approximations
Fields of Research : 01 Mathematical Sciences > 0103 Numerical and Computational Mathematics > 010302 Numerical Solution of Differential and Integral Equations
01 Mathematical Sciences > 0102 Applied Mathematics > 010201 Approximation Theory and Asymptotic Methods
08 Information and Computing Sciences > 0802 Computation Theory and Mathematics > 080205 Numerical Computation
Socio-Economic Objective: E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
URI: http://eprints.usq.edu.au/id/eprint/23204

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