Interpolants for Runge-Kutta formulas
ACM Transactions on Mathematical Software (TOMS)
Natural continuous extensions of Runge-Kutta formulas
Mathematics of Computation
Practical aspects of interpolation in Runge-Kutta codes
SIAM Journal on Scientific and Statistical Computing
Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants
Applied Mathematics and Computation
Rosenbrook methods for differential algebraic equations
Numerische Mathematik
Singular perturbation analysis of linear systems with scalar quantized control
Automatica (Journal of IFAC)
Singular perturbation methods for ordinary differential equations
Singular perturbation methods for ordinary differential equations
A Second-Order Rosenbrock Method Applied to Photochemical Dispersion Problems
SIAM Journal on Scientific Computing
Solving Ordinary Differential Equations with Discontinuities
ACM Transactions on Mathematical Software (TOMS)
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)
Comparison of the asymptotic stability properties for two multirate strategies
Journal of Computational and Applied Mathematics
Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
SIAM Journal on Numerical Analysis
Fundamental matrix solutions of piecewise smooth differential systems
Mathematics and Computers in Simulation
Exponentially fitted two-step hybrid methods for y″=f(x,y)
Journal of Computational and Applied Mathematics
A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
Journal of Computational and Applied Mathematics
General linear methods for y˝=f(y(t))
Numerical Algorithms
Applied Numerical Mathematics
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In this paper we study the numerical solution of a discontinuous differential system by a Rosenbrock method. We also focus on one-sided approach in the context of Rosenbrock schemes, and we suggest a technique based on the use of continuous extension, in order to locate the event point, with an application to discontinuous singularly perturbed systems.