We propose a model order reduction (MOR) approach for networks containing simple and complex components modeled by linear ODE and nonlinear PDE systems respectively. These systems are coupled through the network topology using the Kirchhoff laws. We consider as application MOR for electrical networks, where semiconductors form the complex components. POD combined with discrete empirical interpo...

Der ständig zunehmende Einsatz verteilter DV-Systeme führt zu einem stark steigenden Bedarf an verteilten Anwendungen. Deren Entwicklung in den verschiedensten Anwendungsfeldern wie Fabrikund Büroautomatisierung ist für die Anwender bislang kaum zu handhaben. Neue Konzepte des Software Engineering sind daher notwendig, und zwar in den drei Bereichen ‘Sprachen’, ‘Werkzeuge’ und ‘Umgebungen’. Obj...

The relationships existing between MP graphs, metabolic P systems, and ODE systems are investigated. Formal results show that every MP system, once derived by its MP graph, results in an ODE system whose solution equals, in the limit, the solution obtained by a non-cooperative MP system that is ODE equivalent to the original one. The freedom of choice of the ODE equivalent from the original MP ...

The solution Zz0,h of ODE driven by some smooth path h is a functional of h. Rough path analysis gives some new continuity theorem for the functional h → Zh. In the proof of [3], first, the solution is constructed on small interval and, iterating the procedure, the solution is constructed on the whole interval. In this procedure, the initial point of the solution in the second small interval is...

3 Example: Differentiating the Lotka-Volterra ODE system 2 3.1 The Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3.2 The derivatives of the Lotka-Volterra ODE system . . . . . . . . . . . . . . . . . . 3 3.3 Integration of the original and augmented Lotka-Volterra ODE system with the Runge-Kutta method . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Integrating various suppliers to satisfy market demand is of great importance for e ective supply chain management. In this paper, we consider the ODE-PDE model of supply chain and apply a classical explicit fourth-order Runge-Kutta scheme for the related ODE model of suppliers. Also, the convergence of the proposed method is proved. Finally a numerical example is studied to demonstrate the acc...

Modeling dynamical systems with ordinary differential equations implies a mechanistic view of the process underlying the dynamics. However in many cases, this knowledge is not available. To overcome this issue, we introduce a general framework for nonparametric ODE models using penalized regression in Reproducing Kernel Hilbert Spaces (RKHS) based on operator-valued kernels. Moreover, we extend...

Dengue is currently the fastest growing vector-borne disease which causes fever, headache, muscle aches, and other flu-like symptoms, affecting 50-100 million people worldwide yearly. Modeling dengue incidence over time is challenging because of multiple virus serotypes, high asymptomaticity, and the limited data availability. Different dengue modeling approaches have been explored in the publi...