On invariant closed curves for one-step methods
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Publication:1822214
DOI10.1007/BF01399697zbMath0617.65082MaRDI QIDQ1822214
Publication date: 1987
Published in: Numerische Mathematik (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/133187
numerical experimentsperiodic orbitone-step methodexplicit Runge-Kutta methodAutonomous differential equationshyperbolic closed orbit
Periodic solutions to ordinary differential equations (34C25) Numerical methods for initial value problems involving ordinary differential equations (65L05) Dynamical systems and ergodic theory (37-XX)
Related Items (32)
General linear methods: Connection to one step methods and invariant curves ⋮ On the discretization of a partial differential equation in the neighborhood of a periodic orbit ⋮ Invariant curves for the discretised van der Pol equation ⋮ Hyperbolic trajectories of time discretizations ⋮ Estimation of the Euler method error on a Riemannian manifold ⋮ Invariant curves of one-step methods ⋮ On spurious fixed points of Runge-Kutta methods ⋮ Using dynamical systems methods to solve minimization problems ⋮ Global dynamics of a discontinuous Galerkin approximation to a class of reaction-diffusion equation ⋮ Various closeness concepts in numerical ODE's ⋮ What do multistep methods approximate? ⋮ A BRIEF SURVEY ON THE NUMERICAL DYNAMICS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS ⋮ On the qualitative behavior of the orbits of a parabolic partial differential equation and its discretization in the neighborhood of a hyperbolic fixed point ⋮ Underlying one-step methods and nonautonomous stability of general linear methods ⋮ Periodic orbits of planar discontinuous system under discretization ⋮ Two concepts for numerical periodic solutions of ODE's ⋮ Periodic orbits of delay differential equations under discretization ⋮ Normal hyperbolicity for flows and numerical methods ⋮ Chain recurrence and discretisation ⋮ Periodic orbits and unstable manifolds for ordinary differential equations ⋮ On a One-Parameter Discrete-Time Z4-Equivariant Cubic Dynamical System ⋮ Periodic solutions of autonomous systems under discretization* ⋮ Upper Semicontinuity of Attractors for Linear Multistep Methods Approximating Sectorial Evolution Equations ⋮ A survey of shadowing methods for numerical solutions of ordinary differential equations ⋮ Unstable manifolds for RFDEs under discretization: The Euler method ⋮ A Lyapunov and Sacker-Sell spectral stability theory for one-step methods ⋮ Runge-Kutta time discretization of reaction-diffusion and Navier-Stokes equations: Nonsmooth-data error estimates and applications to long-time behaviour ⋮ Persistence of invariant sets for dissipative evolution equations ⋮ Invariant curves for variable step size integrators ⋮ Consistency of local dynamics and bifurcation of continuous-time dynamical systems and their numerical discretizations ⋮ Topological conjugacy of discrete time-map and Euler discrete dynamical systems generated by a gradient flow on a two-dimensional compact manifold ⋮ Dynamic properties of the local linearization method for initial value problems.
Cites Work
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- Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
- Invariant curves of one-step methods
- Two concepts for numerical periodic solutions of ODE's
- Invariant curves for numerical methods
- On the Numerical Approximation of Phase Portraits Near Stationary Points
- Periodic solutions of finite difference equations
- Stable Attracting Sets in Dynamical Systems and in Their One-Step Discretizations
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