An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems
نویسندگان
چکیده
منابع مشابه
Embedded 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 کاملTrigonometrically-fitted explicit four-stage fourth-order Runge–Kutta–Nyström method for the solution of initial value problems with oscillatory behavior
An explicit trigonometrically-fitted Runge–Kutta–Nyström (ETFRKN) method is constructed in this paper based on Simos technique, which exactly integrates initialvalue problems whose solutions are linear combinations of functions of the form e and e−iwx or equivalently sin(wx) and cos(wx) with w > 0 the principal frequency of the problem. The numerical results show the efficacy of the new method ...
متن کاملTrigonometrically fitted two-step obrechkoff methods for the numerical solution of periodic initial value problems
In this paper, we present a new two-step trigonometrically fitted symmetric Obrechkoff method. The method is based on the symmetric two-step Obrechkoff method, with eighth algebraic order, high phase-lag order and is constructed to solve IVPs with periodic solutions such as orbital problems. We compare the new method to some recently constructed optimized methods from the literature. The numeri...
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 کاملZero-Dissipative Explicit Runge-Kutta Method for Periodic Initial Value Problems
Abstract—In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing ...
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 2017