A Fourth Algebraic Order Explicit Trigonometrically- Fitted Modified Runge-Kutta Method for the Numerical Solution of Periodic IVPs

Trigonometrically-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 ...

An Embedded 4(3) Pair of Explicit Trigonometrically-Fitted Runge-Kutta-Nyström Method for Solving Periodic Initial Value Problems

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...

Fourth-order symplectic exponentially-fitted modified Runge-Kutta methods of the Gauss type: a review

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 cons...

Trigonometrically 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...