Open Access

ABSTRACT

Solving Partial Differential Equations With Point Collocation And One-Dimensional Integrated Interpolation Schemes

N. Mai-Duy¹, T. Tran-Cong¹

1 Computational Engineering and Science Research Centre (CESRC), Faculty of Engineering and Surveying, The University of Southern Queensland, QLD 4350, Australia

The International Conference on Computational & Experimental Engineering and Sciences 2007, 3(3), 127-132. https://doi.org/10.3970/icces.2007.003.127

Abstract

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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