Given a linear variable coefficient DAE, the logarithmic norm a a matrix pencil related to the pencil (A(t), B(t)) allow us to determine the contractivity of ||A(t)x(t)||. When algebraically stable Runge-Kutta methods are used for DAEs, the contractivity for ||A_n+1x_n+1|| is not longer maintained for all stepsize. A new approach for Runge-Kutta methods that preserve this contractivity property can be defined. In this talk we will speak about the advantages and drawbacks of this new approach.

MINISIMPOSIUM SESSION: 13. Numerical methods for DAEs