Numerical Shadowing Near Hyperbolic Trajectories
نویسندگان
چکیده
منابع مشابه
Rigorous Shadowing of Numerical
Rigorous Shadowing of Numerical Solutions of Ordinary Di erential Equations by Containment Wayne Brian Hayes Doctor of Philosophy Graduate Department of Computer Science University of Toronto 2001 An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE ...
متن کاملRigorous Shadowing of Numerical Solutionsof
An exact trajectory of a dynamical system lying close to a numerical trajectory is called a shadow. We present a general-purpose method for proving the existence of nite-time shadows of numerical ODE integrations of arbitrary dimension in which some measure of hyperbolicity is present and there is either 0 or 1 expanding modes, or 0 or 1 contracting modes. Much of the rigor is provided automati...
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A new paradigm for numerically approximating trajectories of an ODE is espoused. We ask for a one to one correspondence between trajectories of an ODE and its discrete approximation. The results enable one, in principal, to compute a trajectory of a discrete approximation, and to use this computation to rigorously prove the existence of a trajectory of the ODE near the discrete trajectory. More...
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ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 1995
ISSN: 1064-8275,1095-7197
DOI: 10.1137/0916068