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Model file Model parser TM integrator Poly ODE 1 Poly ODE 2 Nonpoly ODE

Hybrid systems are dynamical systems which exhibit both continuous flow and discrete jumps. They are natural modeling formalism for the systems composed of a discrete controller interacting with a physical environment. Since hybrid systems often appear in safetycritical situations, it is non-trivial to study their behavior. A typical way to do that is to explore the reachable state space of a h...

On an ODE from forced coating ow

Parallel ODE solvers based on block BVMs

In this paper we deal with Boundary Value Methods (BVMs), which are methods recently introduced for the numerical approximation of initial value problems for ODEs. Such methods, based on linear multistep formulae (LMF), overcome the stability limitations due to the well-known Dahlquist barriers, and have been the subject of much research in the last years. This has led to the definition of a ne...

C Dependence on Initial Conditions for ODE

Lemma 0.1 Let (X, d1) and (Y, d2) be metric spaces. Form the metric space (X × Y, d) where d ((x1, y1), (x2, y2)) = d1(x1, x2) + d2(y1, y2). Suppose that for each x ∈ X we have a function ux ∈ Cb(Y ), the space of bounded continuous functions from Y to R . (Here l is fixed.) Suppose moreover that for each x0 ∈ X, lim x→x0 ‖ux − ux0‖ = 0. (Here ‖‖ denotes sup norm on Y .) For x ∈ X, y ∈ Y , put ...

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