Efficient integration of strangeness-free non-stiff differential-algebraic equations by half-explicit methods

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.