High-order Adaptive Method for Computing Two-dimensional Invariant Manifolds of Maps
نویسندگان
چکیده
We present efficient and accurate numerical methods for computing invariant manifolds of maps which arise in the study of dynamical systems. In order to decrease the number of points needed to compute a given surface, we propose using higher-order approximation techniques developed for the field of computer-aided geometric design (CAGD). We use Bézier curves and triangles, fundamental objects in surface design, to create adaptive method. The method is based on tolerance conditions derived from properties of triangular Bézier patches. We develop and test the method for an ordinary parametric surface and adapt it to compute invariant manifolds of three-dimensional maps.
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