Arbitrary high-order methods for one-sided direct event location in discontinuous differential problems with nonlinear event function

Abstract

In this paper we are concerned with numerical methods for the one-sided event location in discontinuous differential problems, whose event function is nonlinear (in particular, of polynomial type). The original problem is transformed into an equivalent Poisson problem, which is effectively solved by suitably adapting a recently devised class of energy-conserving methods for Poisson systems. The actual implementation of the methods is fully discussed, with a particular emphasis to the problem at hand. Some numerical tests are reported, to assess the theoretical findings.

arXiv comment14 pages, 1 figure, 2 tables

References in corpus (7)

• A note on the efficient implementation of Hamiltonian BVMs
• Analisys of Hamiltonian Boundary Value Methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
• Efficient implementation of Gauss collocation and Hamiltonian Boundary Value Methods
• Analysis of Energy and QUadratic Invariant Preserving (EQUIP) methods
• Functionally-fitted energy-preserving integrators for Poisson systems
• Arbitrarily high-order energy-conserving methods for Poisson problems
• Efficient implementation of Radau collocation methods