B. Karasozen, S. Somali

Asymptotic expansions of the global error of iterated defect correction (IDeC) techniques based on the implicit Euler method for linear differential-algebraic equations (dae's) of arbitrary index are analyzed. The dependence of the maximum attainable
convergence order on the degree of the interpolating polynomial, the number of defect correction steps, and on the index of the differential-algebraic system is given. The effciency of the IDeC method and extrpolation is compared on the basis of numerical experiments and comparing computational cost for both methods. Linear time-varying differential-algebraic equations are investigated by presenting numerical results and extending theoretical results for constant coefficient to these problems.

Keywords: Differential-algebraic equations, implicit Euler method, iterated  defect correction methods, extrapolation