The sequential regularization method (SRM) is a dynamic iterative method for higher index differential-algebraic equations (DAEs). Unlike usual regularization, the regularized problem is less stiff and then non-stiff solvers can possibly be used. The SRM has been successfully applied to many practical problems such as large constrained mechanical multi-body systems, incompressible Navier-Stokes equations, miscible displacement in porous reservoir, etc. The number of SRM iterations is roughly equal to the order of the numerical method we use in each dynamic iteration. In this talk we propose a predicted SRM to reduce the number of iterations to one. Error analysis is given for explicit Runge-Kutta methods. Extrapolation formulas or half-explicit methods for DAEs can be used as a predictor whereas the SRM serves as a corrector for possibly unstable solution obtained by extrapolation formulas or half-explicit methods. Implementation techniques of dynamic iterative methods can be applied to implement the SRM. On the other hand, the SRM provides different insight on designing dynamic iterations. Some numerical demonstrations are carried out.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs