Closed Newton–Cotes trigonometrically-fitted formulae of high order for long-time integration of orbital problems
نویسندگان
چکیده
منابع مشابه
High-order closed Newton-Cotes trigonometrically-fitted formulae for long-time integration of orbital problems
The connection between closed Newton-Cotes, trigonometrically-fitted differential methods and symplectic integrators is investigated in this paper. It is known from the literature that several one step symplectic integrators have been obtained based on symplectic geometry. However, the investigation of multistep symplectic integrators is very poor. Zhu et al. (1996) presented the well known ope...
متن کاملA New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation
In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...
متن کاملHigh Order Phase-fitted Discrete Lagrangian Integrators for Orbital Problems
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase fitted numerical methods for ordinary differential equations. Moreover, an efficient method for frequency evaluation is proposed based on the eccentricities of th...
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 کاملTrigonometrically-fitted second derivative method for oscillatory problems
ABSTRACT A continuous Trigonometrically-fitted Second Derivative Method (CTSDM) whose coefficients depend on the frequency and stepsize is constructed using trigonometric basis functions. A discrete Trigonometrically-fitted second derivative method (TSDM) is recovered from the CTSDM as a by-product and applied to solve initial value problems (IVPs) with oscillating solutions. We discuss the sta...
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: Applied Mathematics Letters
سال: 2009
ISSN: 0893-9659
DOI: 10.1016/j.aml.2009.04.008