Discretization of Poincaré map
نویسندگان
چکیده
We analytically study the relationship between the Poincaré map and its one step discretization. Error estimates are established depending basically on the right hand side function of the investigated ODE and the given numerical scheme. Our basic tool is a parametric version of a Newton–Kantorovich type methods. As an application, in a neighborhood of a non-degenerate periodic solution a new type of step-dependent, uniquely determined, closed curve is detected for the discrete dynamics.
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