Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants
Applied Mathematics and Computation
Numerical methods for ordinary differential systems: the initial value problem
Numerical methods for ordinary differential systems: the initial value problem
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Sliding Modes in Solving Convex Programming Problems
SIAM Journal on Control and Optimization
Control and simulation of hybrid systems
Nonlinear Analysis: Theory, Methods & Applications
Rigid-Body Dynamics with Friction and Impact
SIAM Review
Linear complementarity systems
SIAM Journal on Applied Mathematics
Solving Ordinary Differential Equations with Discontinuities
ACM Transactions on Mathematical Software (TOMS)
Accurate Event Detection for Simulating Hybrid Systems
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
An asynchronous integration and event detection algorithm for simulating multi-agent hybrid systems
ACM Transactions on Modeling and Computer Simulation (TOMACS)
A state event detection algorithm for numerically simulating hybrid systems with model singularities
ACM Transactions on Modeling and Computer Simulation (TOMACS)
An event-driven method to simulate Filippov systems with accurate computing of sliding motions
ACM Transactions on Mathematical Software (TOMS)
Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
SIAM Journal on Numerical Analysis
Fast switches in relay feedback systems
Automatica (Journal of IFAC)
Applied Numerical Mathematics
Original article: Rosenbrock-type methods applied to discontinuous differential systems
Mathematics and Computers in Simulation
Optimal solution of a class of non-autonomous initial-value problems with unknown singularities
Journal of Computational and Applied Mathematics
A comparison of Filippov sliding vector fields in codimension 2
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
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 teacher, always ready to discuss with his students, able to give them profound and interesting suggestions. Here, we present a survey of numerical methods for differential systems with discontinuous right hand side. In particular, we will review methods where the discontinuities are detected by using an event function (so-called event driven methods) and methods where the discontinuities are located by controlling the local errors (so-called time-stepping methods). Particular attention will be devoted to discontinuous systems of Filippov's type where sliding behavior on the discontinuity surface is allowed.