Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation

International audienceIn this paper, we propose a novel approach to bound the local truncation error based on the order condition which is usable for explicit and implicit Runge-Kutta methods

ARCH-COMP19 Category Report: Continuous and hybrid systems with nonlinear dynamics

We present the results of a friendly competition for formal verification of continuous and hybrid systems with nonlinear continuous dynamics. The friendly competition took place as part of the workshop Applied Verification for Continuous and Hybrid Systems (ARCH) in 2019. In this year, 6 tools Ariadne, CORA, DynIbex, Flow*, Isabelle/HOL, and JuliaReach (in alphabetic order) participated. They are applied to solve reachability analysis problems on four benchmark problems, one of them with hybrid dynamics. We do not rank the tools based on the results, but show the current status and discover the potential advantages of different tools

Validated Computation of the Local Truncation Error of Runge-Kutta Methods with Automatic Differentiation

International audienceA novel approach to bound the local truncation error of explicit and implicit Runge-Kutta methods is presented. This approach takes its roots in the modern theory of Runge-Kutta methods, namely the order condition theorem, defined by John Butcher in the 60's. More precisely, our work is an instance, for Runge-Kutta methods, of the generic algorithm defined by Ferenc Bartha and Hans Munthe-Kaas in 2014 which computes B-series with automatic differentiation techniques. In particular, this specialised algorithm is combined with interval analysis tools to define validated numerical integration methods based on Runge-Kutta methods