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

Jay, L. O.

BIT 43, No. 1, 93-106 (2003).

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.

Reviewer: Emil Minchev (Chiba)

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

Keywords:

differential-algebraic equations; index 2; Lobatto coefficients; mechanical systems; implicit Runge-Kutta methods; superconvergence