Order Results for Implicit Runge–Kutta Methods Applied to Differential/Algebraic Systems

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  • LPL. R. Petzold
    L. R. Petzold
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Abstract
In this paper we study the order, stability and convergence properties of implicit Runge–Kutta methods applied to a relatively simple class of nonlinear differential/algebraic systems. These methods often do not attain the same order of accuracy for differential/algebraic systems as they do for purely differential systems. We derive a set of order conditions which the method coefficients should satisfy in addition to the usual order conditions to ensure a given order of accuracy, and we present results on the stability and convergence properties of these methods.

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