Verified Simulation of ODEs and DAEs in ValEncIA-IVP.

Abstract

ValEncIA-IVP is a verified solver for initial value problems for sets of ordinary differential equations which determines guaranteed enclosures of all reachable states. In this paper, we present its new features which allow for a wider application domain. They also improve the performance of ValEncIA-IVP. Especially for the simulation of asymptotically stable systems, we present a new exponential enclosure technique which describes contracting state enclosures. Besides, computation of differential sensitivities as well as verified solution approaches for sets of differential-algebraic equations are introduced.