We present a stable and convergent method for solving initial value problems based on the use of differentiation matrices obtained by Lagrange interpolation. This implicit multistep-like method is easy-to-use and performs pretty well in the solution of mildly stiff problems and it can also be applied directly to differential problems in the complex plane.

Exponential integrators have enjoyed a resurgence of interest in recent years, but there is still limited understanding of how their performance compares with state-of-art integrators most notably the commonly used Newton-Krylov implicit methods. In this paper we present comparative performance analysis of Krylov-based exponential, implicit and explicit integrators on a suite of stiff test prob...

We develop a new high order accurate time-discretisation technique for initial value problems. We focus on problems that originate from a space discretisation using high order finite difference methods on summation-by-parts form with weak boundary conditions, and extend that technique to the time-domain. The new timediscretisation method is global and together with the approximation in space, i...