Practical symplectic partitioned Runge–Kutta and Runge–Kutta–Nyström methods
نویسندگان
چکیده
منابع مشابه
University of Cambridge Numerical Analysis Reports Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods Practical Symplectic Partitioned Runge{kutta and Runge{kutta{nystrr Om Methods
We present new symmetric fourth and sixth-order symplectic Partitioned Runge{ Kutta and Runge{Kutta{Nystrr om methods. We studied compositions using several extra stages, optimising the eeciency. An eeective error, E f , is deened and an extensive search is carried out using the extra parameters. The new methods have smaller values of E f than other methods found in the literature. When applied...
متن کاملStability of Explicit Symplectic Partitioned Runge-Kutta Methods
A numerical method for solving Hamiltonian equations is said to be symplectic if it preserves the symplectic structure associated with the equations. Various symplectic methods are widely used in many fields of science and technology. A symplectic method preserves an approximate Hamiltonian perturbed from the original Hamiltonian. It theoretically supports the effectiveness of symplectic method...
متن کاملEffective order strong stability preserving RungeKutta methods
We apply the concept of effective order to strong stability preserving (SSP) explicit Runge–Kutta methods. Relative to classical Runge–Kutta methods, effective order methods are designed to satisfy a relaxed set of order conditions, but yield higher order accuracy when composed with special starting and stopping methods. The relaxed order conditions allow for greater freedom in the design of ef...
متن کاملOn Higher-order Semi-explicit Symplectic Partitioned Runge-kutta Methods for Constrained Hamiltonian Systems
In this paper we generalize the class of explicit partitioned Runge-Kutta (PRK) methods for separable Hamiltonian systems to systems with holonomic constraints. For a convenient analysis of such schemes, we rst generalize the backward error analysis for systems in I R m to systems on manifolds embedded in I R m. By applying this analysis to constrained PRK methods, we prove that such methods wi...
متن کاملPartitioned Sparse A-1 Methods
This paper solves the classic Ax=b problem by constructing factored components of the inverses of L and U, the triangular factors of A. The number of additional fill-ins in the partitioned inverses of L and U can be made zero. The number of partitions is related to the path length of sparse vector methods. Allowing some fill-in in the partitioned inverses of L and U results in fewer partitions....
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 2002
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(01)00492-7