Half-explicit Runge-Kutta methods for differential-algebraic systems of index 2
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Applied Numerical Mathematics
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Differential-Algebraic Systems: Analytical Aspects and Circuit Applications
Advances in Computational Mathematics
SIAM Journal on Numerical Analysis
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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 multistep 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-valued DAEs which arise in the numerical computation of spectral intervals for DAEs. Numerical experiments illustrate the theoretical results.