This survey article addresses the class of continuous-time systems where a system modeled
by ordinary differential equations is coupled with a static or time-varying set-valued operator …

The paper describes different approaches to generalize the trapezoidal method to fractional
differential equations. We analyze the main theoretical properties and we discuss …

Discontinuities are encountered when objects collide, when decisions are made, when
switches are turned on or off, when light and sound refract as they pass between different …

This work is dedicated to the memory of Donato Trigiante who has been the first teacher of
Numerical Analysis of the second author. The authors remember Donato as a generous …

Abstract This paper introduces Finite Elements with Switch Detection (FESD), a numerical
discretization method for nonsmooth differential equations. We consider the Filippov …

If a set of ordinary differential equations is discontinuous along some threshold, solutions
can be found that are continuous, if sometimes multivalued. We show the extent to which …

Differential equations that switch between different modes of behavior across a surface of
discontinuity are used to model, for example, electronic switches, mechanical contact …

As mathematics is applied to model ever new problems in engineering and the life sciences,
increasing use is being made of systems that switch between different sets of equations on …

We develop a tractable model for studying strategic interactions between learning
algorithms. We uncover a mechanism responsible for the emergence of algorithmic …

This paper introduces a novel time-freezing reformulation and numerical methods for
optimal control of complementarity Lagrangian systems (CLS) with state jumps. We cover …