Interpolation strategies in repeated Richardson extrapolation

Issue title: Some highlights on fuzzy systems and data mining

Guest editors: Shilei Sun, Silviu Ionita, Eva Volná, Andrey Gavrilov and Feng Liu

Article type: Research Article

Authors: Zhang, Cong^a | Zhang, Jun^{b; *}

Affiliations: [a] School of Mathematics and Computer Science, Wuhan Polytechnic University, Wuhan, Hubei, China | [b] Department of Computer Science, University of Kentucky, Lexington, KY, USA

Correspondence: [*] Corresponding author. Jun Zhang, Department of Computer Science, University of Kentucky, Lexington, KY 40506-0633, USA. Tel.: +1 8592573961; Fax: +1 8592571505; jzhang@cs.uky.edu

Abstract: We discuss the interpolation strategies related to Richardson extrapolation and repeated Richardson extrapolation. We emphasize that, in most computations, the interest is in obtaining accurate solution on the current computational grid, not that on the coarse level grids on which the extrapolated solutions reside. We tackle the interpolation issue that has largely been overlooked in Richardson extrapolation related applications. We present numerical experiments to support our analysis.

Keywords: Computational grid, finite difference scheme, Richardson extrapolation, interpolation, high order solution

DOI: 10.3233/JIFS-169177

Journal: Journal of Intelligent & Fuzzy Systems, vol. 31, no. 6, pp. 2935-2939, 2016