Title: Error analysis of Parallel Multivalue Hybrid Methods for index-2 Differential-Algebraic Equations

Authors: Aiguo Xiao, Jialan Liu

Addresses: School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, PR China. ' School of Mathematics and Computational Science, Hunan Key Laboratory for Computation and Simulation in Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, PR China

Abstract: The main purpose of this paper is to present some convergence results of a class of Parallel Multivalue Hybrid Methods (PMHMs) for semi-explicit index-2 differential-algebraic equations. Some numerical examples confirm our theoretical results and show that the computed orders of the 2-step 2-order PMHM (PMHM2) and the 3-step 3-order PMHM(PMHM3) are higher than the corresponding theoretical orders and the corresponding computed orders of the 2-step 2-order BDF method and the 3-step 3-order BDF method. This interesting phenomenon is due to the apparently smaller residual error constants of PMHM2 and PMHM3 than those of the corresponding BDF methods.

Keywords: differential algebraic equations; DAEs; index 2; parallel multivalue hybrid methods; PMHMs; convergence; error analysis.

DOI: 10.1504/IJCSM.2008.019727

International Journal of Computing Science and Mathematics, 2008 Vol.2 No.1/2, pp.181 - 199

Published online: 25 Jul 2008 *

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