Implicit runge-kutta methods for differential inclusions

DOI10.1080/01630569108816411zbMath0712.65072OpenAlexW2057805982MaRDI QIDQ3197233

Alois E. Kastner-Maresch

Publication date: 1991

Published in: Numerical Functional Analysis and Optimization (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/01630569108816411

zbMATH Keywords

differential inclusionsstiff differential equationsimplicit Runge-Kutta methodsdiscontinuous right-hand sideshigher order of convergence

Mathematics Subject Classification ID

Ordinary differential inclusions (34A60) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Multiple scale methods for ordinary differential equations (34E13)

Related Items (13)

The method of uniform monotonous approximation of the reachable set border for a controllable system ⋮ Classification of Hidden Dynamics in Discontinuous Dynamical Systems ⋮ Continuous selection of the solution map for one-sided Lipschitz differential inclusions ⋮ Fixed set iterations for relaxed Lipschitz multimaps. ⋮ Algorithm of uniform filling of nonlinear dynamic system reachable set based on maximin problem solution ⋮ On a possible approximation of discontinuous dynamical systems. ⋮ A Filippov approximation theorem for strengthened one-sided Lipschitz differential inclusions ⋮ On Numerical Integration of Discontinuous Dynamical Systems ⋮ On a class of non-smooth dynamical systems: a sufficient condition for smooth versus non-smooth solutions ⋮ Algorithm for piecewise-linear approximation of the reachable set boundary ⋮ On the uniqueness of solutions to a class of discontinuous dynamical systems ⋮ Discrete Filippov-Type Stability for One-Sided Lipschitzian Difference Inclusions ⋮ Unnamed Item

Cites Work

• A high accuracy method for solving ODEs with discontinuous right-hand side
• The order of B-convergence of the Gaussian Runge-Kutta method
• A study of B-convergence of Runge-Kutta methods
• B-convergence of the implicit midpoint rule and the trapezoidal rule
• The dichotomy of stiffness: Pragmatism versus theory
• Converging multistep methods for initial value problems involving multivalued maps
• One-step methods of any order for ordinary differential equations with discontinuous right-hand sides
• Stability Properties of Implicit Runge–Kutta Methods
• Order Results for Implicit Runge–Kutta Methods Applied to Stiff Systems
• On the Convergence of a One-step Method for the Numerical Solution of an Ordinary Differential Inclusion
• On the discrete convergence of multistep methods for differential inclusions
• Zur Integration über Unstetigkeiten in gewöhnlichen Differentialgleichungen
• Non-linear stability of a general class of differential equation methods
• Inverse stability and convergence of difference approximations for boundary value problems for differential inclusions
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