Solving Ordinary Differential Equations with Discontinuities

Charles William Gear (1) , Ole Østerby (2)

1 UIUC - University of Illinois at Urbana-Champaign [Urbana]
2 Aarhus University [Aarhus]

Automatic codes for differential equations can be inadequate when the solutions have discontinuities. If the user provides an external indicator for discontinuities (e.g., a switching function whose sign changes indicate discontinuities), a code can be more efficient. A technique for detection and location of a discontinuity is discussed which can be implemented when such indicators are not practical. It estimates the order and magnitude of the discontinuity and hence the stepsize which keeps the error under control while stepping over the discontinuity.

Mots clés: multistep; differential equations; singularities; discontinuities

Domaines: Mathématiques [math]; Systèmes dynamiques [math.DS]

Charles William Gear, Ole Østerby. Solving Ordinary Differential Equations with Discontinuities. ACM Transactions on Mathematical Software, 1984, 10 (1), pp.23-44. ⟨10.1145/356068.356071⟩. ⟨hal-01928590⟩