Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The stabilization of linear multistep methods for constrained mechanical systems
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Applied Numerical Mathematics
Journal of Computational and Applied Mathematics
Stability preserving integration of index-2 DAEs
Applied Numerical Mathematics
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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.