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Solution of index 2 implicit differential-algebraic equations by Lobatto Runge-Kutta methods. (English) Zbl 1023.65085

The author studies the numerical solutions of the following system of implicit differential-algebraic equations \[ a^\prime(t,y) = f(t,y,z), \]
\[ 0 = g(t,y) \] using a class of super partitioned additive Runge-Kutta methods. Superconvergence of optimal order \(2s-2\) for the \(s\)-stage Lobatto families is shown.

MSC:

65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
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