Uses of Verified Methods for Solving Non-Smooth Initial Value Problems

Many system types in engineering require mathematical models involving non-differentiable or discontinuous functions. Such system models are often sensitive to round-off errors. Their parameters might be uncertain due to impreciseness in measurements or lack of knowledge. Therefore, interval methods represent a straightforward choice for verified analysis of such systems. However, application of existing interval methods to reallife scenarios is challenging, since they might provide overly conservative enclosures of exact solutions. In this paper, we analyze a simple method to obtain meaningful solution enclosures. First, we identify important types of non-smooth applications along with their corresponding solution definitions. After that, we provide an overview of existing methods for verified enclosure of exact solutions to non-smooth IVPs. Next, we introduce a simple enclosure strategy which relies on basically the same techniques as in the smooth case. Finally, we demonstrate the applicability of the simple method using several examples, and compare the results to those produced by the existing techniques.