A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side

DOI10.1016/j.cam.2012.02.011zbMath1246.65111OpenAlexW2152775880MaRDI QIDQ433943

Luciano Lopez, Luca Dieci

Publication date: 9 July 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2012.02.011

zbMATH Keywords

numerical examplesdifferential systemssurvey articlediscontinuous ODEsordinary differential equations (ODEs)discontinuous systems of Filippov's typeevent driven methodsinitial value problems (IVPs)one-step and multistep methodstime-stepping methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (43)

On a nonlocal extension of differentiation ⋮ Into higher dimensions for nonsmooth dynamical systems ⋮ Numerical event location techniques in discontinuous differential algebraic equations ⋮ Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function ⋮ On the mathematical basis of solid friction ⋮ Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system ⋮ A critical case for the spiral stability for \(2\times 2\) discontinuous systems and an application to recursive neural networks ⋮ Efficient solution of IVPs with right-hand sides having discontinuities on an unknown hypersurface ⋮ Event-driven integration of linear structural dynamics models under unilateral elastic constraints ⋮ Coincidence of the Gelig-Leonov-Yakubovich, Filippov, and Aizerman-Pyatnitskiy definitions ⋮ Smooth to discontinuous systems: a geometric and numerical method for slow-fast dynamics ⋮ Periodic orbits of planar discontinuous system under discretization ⋮ Causal modeling in impulsive systems: a new rigorous non-standard analysis approach ⋮ Dynamic flux balance analysis with nonlinear objective function ⋮ Optimal solution of a class of non-autonomous initial-value problems with unknown singularities ⋮ An unconditionally stable explicit finite element algorithm for coupled hydromechanical problems of soil mechanics in pseudo‐static conditions ⋮ Markovian solutions to discontinuous ODEs ⋮ Uniqueness of Filippov sliding vector field on the intersection of two surfaces in \(\mathbb R^3\) and implications for stability of periodic orbits ⋮ Conservative integrators for piecewise smooth systems with transversal dynamics ⋮ On Numerical Integration of Discontinuous Dynamical Systems ⋮ One-sided direct event location techniques in the numerical solution of discontinuous differential systems ⋮ On Filippov solutions of discontinuous DAEs of index 1 ⋮ Complexity of the derivative-free solution of systems of IVPs with unknown singularity hypersurface ⋮ Trapezoidal methods for fractional differential equations: theoretical and computational aspects ⋮ A general framework for the numerical solution of second order odes ⋮ The numerical solution of Richards' equation by means of method of lines and ensemble Kalman filter ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ An adaptive and explicit fourth order Runge-Kutta-Fehlberg method coupled with compact finite differencing for pricing American put options ⋮ Analysis of a model for precipitation and dissolution coupled with a Darcy flux ⋮ Solving systems of IVPs with discontinuous derivatives-numerical experiments ⋮ A model for the hepatic glucose metabolism based on Hill and step functions ⋮ Sliding integration with no projection ⋮ Numerical analysis of the dynamics of rigid blocks subjected to support excitation ⋮ A comparison of Filippov sliding vector fields in codimension 2 ⋮ Optimal adaptive solution of piecewise regular systems of IVPs with unknown switching hypersurface ⋮ Exponential quadrature rules for linear fractional differential equations ⋮ Fractional-order PWC systems without zero Lyapunov exponents ⋮ Non-degenerate maximum principle for optimal control problems with discontinuous right-hand side ⋮ A note on attractivity for the intersection of two discontinuity manifolds ⋮ Null space gradient flows for constrained optimization with applications to shape optimization ⋮ On the linear stability of a vortex pair equilibrium on a Riemann surface of genus zero ⋮ Revised exponentially fitted Runge-Kutta-Nyström methods ⋮ An efficient algorithm for solving piecewise-smooth dynamical systems

Uses Software

• RODAS

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Qualitative simulation of genetic regulatory networks using piecewise-linear models
• On the continuous extension of Adams-Bashforth methods and the event location in discontinuous ODEs
• Dynamics and bifurcations of non-smooth mechanical systems
• Computing breaking points in implicit delay differential equations
• Effective solution of discontinuous IVPs using a Runge-Kutta formula pair with interpolants
• Strong contractivity properties of numerical methods for ordinary and delay differential equations
• Sliding modes in control and optimization. Transl. from the Russian
• One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
• Efficient integration over discontinuities in ordinary differential equation simulations
• Fast switches in relay feedback systems
• The simplex method for nonlinear sliding mode control
• On the solution of discontinuous IVPs by adaptive Runge--Kutta codes
• Event location for ordinary differential equations
• Bifurcations of dynamical systems with sliding: derivation of normal-form mappings
• Analysis and generic properties of gene regulatory networks with graded response functions
• Piecewise-linear models of genetic regulatory networks: equilibria and their stability
• Piecewise-smooth dynamical systems. Theory and applications
• Simulation and stability analysis of impacting systems with complete chattering
• Sliding motion on discontinuity surfaces of high co-dimension. A construction for selecting a Filippov vector field
• Numerical methods for nonsmooth dynamical systems. Applications in mechanics and electronics
• Two-parameter degenerate sliding bifurcations in Filippov systems
• Regularization of discontinuous vector fields on \({\mathbb{R}^3}\) via singular perturbation
• Solving Ordinary Differential Equations with Discontinuities
• A state event detection algorithm for numerically simulating hybrid systems with model singularities
• An event-driven method to simulate Filippov systems with accurate computing of sliding motions
• Sliding Motion in Filippov Differential Systems: Theoretical Results and a Computational Approach
• Control and simulation of hybrid systems
• Sliding Modes in Solving Convex Programming Problems
• A class of piecewise linear differential equations arising in biological models
• An analysis of a class of neural networks for solving linear programming problems
• Linear Complementarity Systems
• An asynchronous integration and event detection algorithm for simulating multi-agent hybrid systems
• One-Parameter Bifurcations in Planar Filippov Systems
• Rigid-Body Dynamics with Friction and Impact
• Limit cycles with chattering in relay feedback systems
• Geometric Numerical Integration
• Bifurcations in nonlinear discontinuous systems

This page was built for publication: A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side