In this paper we present necessary and sufficient conditions for Runge-Kutta methods to be
contractive. We consider not only unconditional contractivity for arbitrary dissipative initial …

It is well known that a necessary condition for the Lax-stability of the method of lines is that
the eigenvalues of the spatial discretization operator, scaled by the time step k, lie within a …

We address the question of convergence of fully discrete Runge-Kutta approximations. We
prove that, under certain conditions, the order in time of the fully discrete scheme equals the …

This article addresses the general problem of establishing upper bounds for the norms of the
nth powers of square matrices. The focus is on upper bounds that grow only moderately (or …

In the past numerical stability theory for initial value problems in ordinary differential
equations has been dominated by the study of problems with simple dynamics; this has …

Over the last few years, great effort has been made to develop high order strong stability
preserving (SSP) Runge–Kutta methods. These methods have a nonlinear stability property …

We introduce a novel, time-efficient adaptive Runge-Kutta computational scheme tailored for
systematically solving linear and nonlinear Volterra-type Integro-Differential Equations …

We construct and analyze robust strong stability preserving IMplicit–EXplicit Runge–Kutta
(IMEX RK) methods for models of flow with diffusion as they appear in astrophysics, and in …

Strong stability (or monotonicity)-preserving time discretization schemes preserve the
stability properties of the exact solution and have proved very useful in scientific and …

An important class of ordinary differential systems is that whose solutions satisfy a
monotonicity property for a given norm. For these problems, a natural requirement for the …