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
نویسندگان
چکیده
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 to several examples they perform up to two orders of magnitude better than previously known method, which is in very good agreement with the values of E f .
منابع مشابه
Eighth-order Explicit Symplectic Runge-kutta-nystrr Om Integrators
We consider the solution of Hamiltonian dynamical systems by constructing eighth-order explicit symplectic Runge-Kutta-Nystrr om integrators. The application of high-order integrators may be important in areas such as in astronomy. They require large number of function evaluations, which make them computationally expensive and easily susceptible to errors. The integrators developed in this pape...
متن کاملBackward Analysis of Numerical
A backward analysis of integration methods, whose numerical solution is a P-series, is presented. Such methods include Runge-Kutta methods, partitioned Runge-Kutta methods and Nystrr om methods. It is shown that the numerical solution can formally be interpreted as the exact solution of a perturbed diierential system whose right-hand side is again a P-series. The main result of this article is ...
متن کاملContinuous Extensions to Nystr
In this work, we consider interpolants for Nystrr om methods, i.e., second order initial value problems. We give a short introduction to the theory behind the discrete methods, and extend some of the work to continuous, explicit Nystrr om methods. Interpolants for continuous, explicit Runge-Kutta methods have been intensively studied by several authors, but there has not been much eeort devoted...
متن کاملSymplectic and symmetric methods for the numerical solution of some mathematical models of celestial objects
In the last years, the theory of numerical methods for system of non-stiff and stiff ordinary differential equations has reached a certain maturity. So, there are many excellent codes which are based on Runge–Kutta methods, linear multistep methods, Obreshkov methods, hybrid methods or general linear methods. Although these methods have good accuracy and desirable stability properties such as A...
متن کاملPreservation of stability properties near fixed points of linear Hamiltonian systems by symplectic integrators
Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.
متن کامل