Invariant manifolds and global error estimates of numerical integration schemes applied to stiff systems of singular perturbation type -- Part I: RK-methods

Summary. For implicit RK-methods applied to singularly perturbed systems of ODEs it is shown that the resulting discrete systems preserve the geometric properties of the underlying ODE. This invariant manifold result is used to derive sharp bounds on the global error of RK-solutions. Received August 26, 1993 / Revised version received May 10, 1994