کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
8902619 1632144 2018 25 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات ریاضیات محاسباتی
پیش نمایش صفحه اول مقاله
Symplectic Runge-Kutta methods for Hamiltonian systems driven by Gaussian rough paths
چکیده انگلیسی
We consider Hamiltonian systems driven by multi-dimensional Gaussian processes in rough path sense, which include fractional Brownian motions with Hurst parameter H∈(1/4,1/2]. We prove that the phase flow preserves the symplectic structure almost surely and this property could be inherited by symplectic Runge-Kutta methods, which are implicit methods in general. If the vector fields satisfy some smoothness and boundedness conditions, we obtain the pathwise convergence rates of Runge-Kutta methods. When vector fields are linear, we get the solvability of the midpoint scheme for skew symmetric cases, and obtain its pathwise convergence rate. Numerical experiments verify our theoretical analysis.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied Numerical Mathematics - Volume 129, July 2018, Pages 120-136
نویسندگان
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