On the spectral operator of parallel iteration for index-3 differential-algebraic systems

Using the spectra properties we study the convergence performance for nonlinear differential algebraic equations of index-3. The new convergence results are obtained. The iterative errors have been estimated. In particular, the iteration algorithms possess inherent parallelism for solving nonlinear differential-algebraic systems. Then a technique on windowing is also presented. This accelerating method could improve the convergence of differential-algebraic systems for longer interval of time integration. A few numerical experiments have tested for the theoretical problems.