On the continuous extension of Adams-Bashforth methods and the event location in discontinuous ODEs

DOI10.1016/J.AML.2011.11.014zbMath1242.65128OpenAlexW2047737228MaRDI QIDQ419132

Marco Berardi, Luciano Lopez

Publication date: 18 May 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2011.11.014

zbMATH Keywords

numerical examplesAdams-Bashforth methodsdiscontinuous differential systemsevent locationNordsieck technique

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (12)

Direct event location techniques based on Adams multistep methods for discontinuous ODEs ⋮ Numerical event location techniques in discontinuous differential algebraic equations ⋮ A critical case for the spiral stability for \(2\times 2\) discontinuous systems and an application to recursive neural networks ⋮ Computational techniques to locate crossing/sliding regions and their sets of attraction in non-smooth dynamical systems ⋮ One-sided direct event location techniques in the numerical solution of discontinuous differential systems ⋮ A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side ⋮ A mixed MoL-TMoL for the numerical solution of the 2D Richards' equation in layered soils ⋮ The numerical solution of Richards' equation by means of method of lines and ensemble Kalman filter ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ Time-transformations for the event location in discontinuous ODEs ⋮ On the equivalence of the continuous Adams-Bashforth method and Nordsieck's technique for changing the step size ⋮ Revised exponentially fitted Runge-Kutta-Nyström methods

Cites Work

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• Event location for ordinary differential equations
• On Numerical Integration of Ordinary Differential Equations
• Natural Continuous Extensions of Runge-Kutta Methods
• Equivalent Forms of Multistep Formulas
• On Nordsieck's method for the numerical solution of ordinary differential equations

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