The numerical solution of higher index differential/algebraic equations by implicit methods. (English) Zbl 0681.65050

Authors’ summary: This paper studies the order, stability, and convergence properties of implicit Runge-Kutta (IRK) methods applied to differential/algebraic systems with index greater than one. These methods do not in general attain the same order of accuracy for higher index differential/algebraic systems as they do for index 1 systems or for purely differential systems. Necessary and sufficient conditions on the method coefficients are derived to ensure that the local and global errors of the method attain a given order of accuracy for higher index linear constant coefficient systems. IRK methods applied to nonlinear semi-explicit index 2 systems are studied, and a sufficient set of conditions is derived which ensures that a method is accurate to a given order for these systems. Finally, some numerical experiments are presented that illustrate the theoretical results and demonstrate the effects of roundoff errors on the solution.
Reviewer: Z.Jackiewicz


65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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