Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nyström Methods for Solving y′′(x)=fx,y,y′
نویسندگان
چکیده
منابع مشابه
Exponentially 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 کاملThree-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 کاملEmbedded 5(4) Pair Trigonometrically-Fitted Two Derivative Runge- Kutta Method with FSAL Property for Numerical Solution of Oscillatory Problems
Based on First Same As Last (FSAL) technique, an embedded trigonometrically-fitted Two Derivative Runge-Kutta method (TDRK) for the numerical solution of first order Initial Value Problems (IVPs) is developed. Using the trigonometrically-fitting technique, an embedded 5(4) pair explicit fifth-order TDRK method with a “small” principal local truncation error coefficient is derived. The numerical...
متن کاملA New Family of Phase-Fitted and Amplification-Fitted Runge-Kutta Type Methods for Oscillators
In order to solve initial value problems of differential equations with oscillatory solutions, this paper improves traditional Runge-Kutta RK methods by introducing frequency-depending weights in the update. New practical RK integrators are obtained with the phase-fitting and amplification-fitting conditions and algebraic order conditions. Two of the new methods have updates that are also phase...
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
ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2018
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2018/7689854