Intrinsic Projection (IP) of Implicit Runge Kutta Methods for Differential Algebraic Equations
Nikita Kapur (University of Iowa, USA.), Laurent Jay
We present the new technique of Intrinsic Projection (IP) for Implicit Runge-Kutta (IRK) Methods applied to differential-algebraic equations (DAEs). IP does not require the accurate evaluation of any additional Jacobian like for standard Projected Implicit Runge-Kutta Methods and is therefore simpler to implement. IP for IRK methods is analyzed for index 2 DAEs, in particular we give results about existence and uniqueness, and some error estimates. For index 2 DAEs IP for IRK methods is shown to lead to the same order of error estimates as standard Projected Implicit Runge-Kutta Methods, but at a lower computational cost. Some preliminary results for index 3 DAEs will also be given.