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

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.