کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4645445 | 1342034 | 2011 | 12 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Explicit symplectic partitioned Runge–Kutta–Nyström methods for non-autonomous dynamics Explicit symplectic partitioned Runge–Kutta–Nyström methods for non-autonomous dynamics](/preview/png/4645445.png)
We consider explicit symplectic partitioned Runge–Kutta (ESPRK) methods for the numerical integration of non-autonomous dynamical systems. It is known that, in general, the accuracy of a numerical method can diminish considerably whenever an explicit time dependence enters the differential equations and the order reduction can depend on the way the time is treated. In the present paper, we demonstrate that explicit symplectic partitioned Runge–Kutta–Nyström (ESPRKN) methods specifically designed for second order differential equations , undergo an order reduction when M=M(t), independently of the way the time is approximated. Furthermore, by means of symmetric quadrature formulae of appropriate order, we propose a different but still equivalent formulation of the original non-autonomous problem that treats the time as two added coordinates of an enlarged differential system. In so doing, the order reduction is avoided as confirmed by the presented numerical tests.
Journal: Applied Numerical Mathematics - Volume 61, Issue 7, July 2011, Pages 832-843