Runge–Kutta methods for DAEs. A new approach

摘要

Given a linear variable coefficient DAE, the logarithmic norm of a pencil related to the original pencil (A(t),B(t)), allows us to determine the contractivity of ∥A(t)x(t)∥. When algebraically stable Runge–Kutta methods are used for DAEs, the contractivity for ∥An+1xn+1∥ is no longer maintained for all stepsize. In this paper we define a new approach for Runge–Kutta methods that preserve contractivity.