The construction of exponentially fitted (EF) two-step hybrid methods for the numerical
integration of oscillatory second-order IVPs is analyzed. These methods integrate exactly …

The construction of a class of nonlinear two-step methods for solving second order
oscillatory IVPs is analyzed. These methods are exact for the linear space generated by the …

The construction of new embedded pairs of explicit Runge–Kutta methods specially adapted
to the numerical solution of oscillatory problems is analyzed. Based on the order conditions …

The construction of high-order exponentially fitted Runge–Kutta–Nyström (EFRKN) methods
of explicit type for the numerical solution of oscillatory differential systems is analyzed …

The construction of optimized explicit two-step hybrid methods for solving orbital problems
and oscillatory second order IVPs is analyzed. These methods have variable coefficients …

In this paper the use of a trigonometrically fitted method to obtain the approximate solutions
of some nonlinear periodic oscillators is presented. A great number of different approaches …

For the approximate solution of the Kepler equations and some related problems, a fourth-
order convergent functionally-fitted block hybrid Falkner method which is based on the …

Abstract Continuous-stage extended Runge-Kutta-Nyström (CSERKN) methods are
proposed and developed for oscillatory problem q ″(t)+ M q (t)= f (q (t)). These new …

It is the purpose of this paper to revise the exponential fitting technique for the numerical
solution of special second order ordinary differential equations (ODEs) y ″= f (x, y), with …

One of the well-known schemes for the direct numerical integration of second-order initial-
value problems is due to Falkner. This paper focuses on the construction of a family of …