Fourth-order symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type: a review
نویسندگان
چکیده
The construction of symmetric and symplectic exponentially-fitted Runge-Kutta methods for the numerical integration of Hamiltonian systems with oscillatory solutions is reconsidered. In previous papers fourth-order and sixth-order symplectic exponentially-fitted integrators of Gauss type, either with fixed or variable nodes, have been derived. In this paper new fourth-order integrators are constructed by making use of the six-step procedure of Ixaru and Vanden Berghe (Exponential fitting, Kluwer Academic Publishers, 2004). Numerical experiments for some oscillatory problems are presented and compared to the results obtained by previous methods. MSC: 65L05,65L06
منابع مشابه
Three-stage two-parameter symplectic, symmetric exponentially-fitted Runge-Kutta methods of Gauss type
We construct an exponentially-fitted variant of the well-known three stage Runge-Kutta method of Gauss-type. The new method is symmetric and symplectic by construction and it contains two parameters, which can be tuned to the problem at hand. Some numerical experiments are given.
متن کاملSymplectic Runge-Kutta-Nyström Methods with Phase-Lag Oder 8 and Infinity
In this work we consider Symplectic Runge Kutta Nyström methods with five stages. A new fourth algebraic order method with phase-lag order eight is presented. Also the symplectic Runge Kutta Nyström of Calvo and Sanz Serna with five stages and fourth order is modified to produce a phase-fitted method. We apply the new methods on several Hamiltonian systems and on the computation of the eigenval...
متن کاملExponentially Fitted Symplectic Runge-Kutta-Nyström methods
In this work we consider symplectic Runge Kutta Nyström (SRKN) methods with three stages. We construct a fourth order SRKN with constant coefficients and a trigonometrically fitted SRKN method. We apply the new methods on the two-dimentional harmonic oscillator, the Stiefel-Bettis problem and on the computation of the eigenvalues of the Schrödinger equation.
متن کاملExponentially Accurate Hamiltonian Embeddings of Symplectic A-stable Runge–kutta Methods for Hamiltonian Semilinear Evolution Equations
We prove that a class of A-stable symplectic Runge–Kutta time semidiscretizations (including the Gauss–Legendre methods) applied to a class of semilinear Hamiltonian PDEs which are well-posed on spaces of analytic functions with analytic initial data can be embedded into a modified Hamiltonian flow up to an exponentially small error. As a consequence, such timesemidiscretizations conserve the m...
متن کاملSymmetric and symplectic exponentially fitted Runge-Kutta methods of high order
Article history: Received 27 April 2010 Received in revised form 2 August 2010 Accepted 19 August 2010 Available online 26 August 2010
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 2009