Diagonally Implicit Symplectic Runge-Kutta Methods with Special Properties
نویسنده
چکیده
The numerical integration of Hamiltonian systems is considered in this paper. Diagonally implicit Symplectic Runge-Kutta methods with special properties are presented. The methods developed have six and seven stages algebraic order up to 5th and dispersion order up to 8th.
منابع مشابه
Diagonally Implicit Symplectic Runge-Kutta Methods with High Algebraic and Dispersion Order
The numerical integration of Hamiltonian systems with oscillating solutions is considered in this paper. A diagonally implicit symplectic nine-stages Runge-Kutta method with algebraic order 6 and dispersion order 8 is presented. Numerical experiments with some Hamiltonian oscillatory problems are presented to show the proposed method is as competitive as the existing same type Runge-Kutta methods.
متن کاملEmbedded Singly Diagonally Implicit Runge-Kutta –Nystrom Method Order 5(4) for the Integration of Special Second Order ODEs
In this paper a new embedded Singly Diagonally Implicit Runge-Kutta Nystrom fourth order in fifth order method for solving special second order initial value problems is derived. A standard set of test problems are tested upon and comparisons on the numerical results are made when the same set of test problems are reduced to first order systems and solved using the existing embedded diagonally ...
متن کاملEmbedded Diagonally Implicit Runge - Kutta Algorithms on Parallel Computers
This paper investigates diagonally implicit Runge-Kutta methods in which the implicit relations can be solved in parallel and are singly diagonalimplicit on each processor. The algorithms are based on diagonally implicit iteration of fully implicit Runge-Kutta methods of high order. The iteration scheme is chosen in such a way that the resulting algorithm is ^(a)-stable or Z,(a)-stable with a e...
متن کاملHigh-Order Implicit Time Integration for Unsteady Compressible Fluid Flow Simulation
This paper presents an overview of high-order implicit time integration methods and their associated properties with a specific focus on their application to computational fluid dynamics. A framework is constructed for the development and optimization of general implicit time integration methods, specifically including linear multistep, Runge-Kutta, and multistep Runge-Kutta methods. The analys...
متن کاملSingly diagonally implicit Runge-Kutta methods with an explicit first stage
The purpose of this paper is to construct methods for solving stiff ODEs, in particular singular perturbation problems. We consider embedded pairs of singly diagonally implicit Runge-Kutta methods with an explicit first stage (ESDIRKs). Stiffly accurate pairs of order 3/2, 4/3 and 5/4 are constructed. AMS Subject Classification: 65L05
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2014