Inscrutable
发表于 2025-3-25 03:48:47
Linear SystemsStability of linear systems by eigenvalue conditions is introduced. Stability conditions for one and two dimensional, as well as general linear systems, are established.
thyroid-hormone
发表于 2025-3-25 08:38:05
Lyapunov FunctionsLyapunov functions are defined and used to investigate the stability of the zero solution to Euler schemes for linear and nonlinear ODEs.
冥想后
发表于 2025-3-25 13:35:58
Dissipative Systems with Steady StatesThe preservation or stability of the zero solution to Euler schemes for dissipative systems is established using Lyapunov functions.
大方一点
发表于 2025-3-25 16:09:04
Saddle Points Under DiscretisationSaddle points for Euler schemes for ODEs are discussed. Numerical stable and unstable manifolds are illustrated through a set of examples, and compared to the stable and unstable manifolds of the ODEs. The shadowing phenomenon is briefly illustrated. Finally, Beyn’s Theorem is presented.
extrovert
发表于 2025-3-25 21:41:28
Dissipative Systems with AttractorsEuler schemes for dissipative ODE systems with attractors are presented and shown to possess numerical attractors that converge to the ODE attractors upper semi continuously. A counterexample shows that the numerical attractor need not convergence lower semi continuously.
替代品
发表于 2025-3-26 02:27:47
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违反
发表于 2025-3-26 05:35:30
Discretisation of an Attractor: General CaseKloeden and Lorenz’s Theorem on the existence of a maximal numerical attractor of one step numerical schemes for general autonomous ODEs with a global attractor is stated and proved.
SHOCK
发表于 2025-3-26 10:06:31
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财主
发表于 2025-3-26 14:01:50
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SNEER
发表于 2025-3-26 18:50:33
Variable Step Size Discretisation of Autonomous AttractorsDiscretising autonomous ODEs with variable step size results in discrete nonautonomous semi-dynamical systems. Numerical omega limit sets for such dynamical systems are constructed and shown to converge to the attractor for the ODEs upper semi continuously.