Efficient integration of matrix-valued non-stiff DAEs by half-explicit methods

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Author(s) : Vu Hoang Linh , Volker Mehrmann

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 16-2011

MSC 2000

65L07 Numerical investigation of stability of solutions
65L80 Methods for differential-algebraic equations

Abstract :
Numerical integration methods for nonlinear differential-algebraic equations (DAEs) in strangeness-free form are studied. In particular, half-explicit methods based on popular explicit methods like one-leg methods, linear multi-step methods, and Runge-Kutta methods are proposed and analyzed. Compared with well-known implicit methods for DAEs, these half-explicit methods demonstrate their efficiency particularly for a special class of semi-linear matrix DAEs which arise in the numerical computation of spectral intervals for DAEs. Numerical experiments illustrate the theoretical results.

Keywords : differential-algebraic equation, strangeness index, half-explicit methods, one-leg methods, linear multi-step methods, Runge-Kutta methods, spectral intervals.