A New Class of Results for the Algebraic Equations of Implicit Runge-Kutta Processes

Publisher Website
Google Scholar
Abstract
We are concerned with the solvability of the discrete equations arising in the use of Runge-Kutta methods. Under suitable assumptions on the RK tableau, we show that in the neighbourhood of a sink (asymptotically stable equilibrium) a unique solution exists for arbitrarily large stepsizes. Furthermore in the neighbourhood of a slowly varying integral curve z = z(t) that attracts neighbouring integral curves of the ODE system, a unique solution of the algebraic equations exists, provided that the stepsize is suitably restricted. This restriction does not depend on the stiffness of the ODEs being integrated.

This publication has 0 references indexed in Scilit: