Multistep Runge-Kutta Methods for solving DAEs

Several methods have been used by some authors to solve Differential Algebraic Equations (DAEs), the methods range from multistep methods such as BDF and EBDF methods to one-step methods such as Runge-Kutta methods. In this paper, we present Multistep Runge-Kutta methods (MRKs) for solving DAEs which are the extension of our previous works for solving ODEs. We discuss fixed stepsize MRKs and Variable Coefficient MRKs. The methods treat the DAEs as problems of the form M y ' = f(x). We implement the MRKs in parallel iteration technique and present some numerical tests