Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Runge-Kutta(-Nystro¨m) methods for ODEs with periodic solutions based on trigonometric polynomials
Applied Numerical Mathematics - Selected papers on eighth conference on the numerical treatment of differential equations 1-5 September 1997, Alexisbad, Germany
Exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics - Special issue on numerical anaylsis 2000 Vol. VI: Ordinary differential equations and integral equations
An embedded pair of exponentially fitted explicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
A 5(3) pair of explicit ARKN methods for the numerical integration of perturbed oscillators
Journal of Computational and Applied Mathematics
Exponentially fitted explicit Runge-Kutta-Nyström methods
Journal of Computational and Applied Mathematics
Runge-Kutta methods adapted to the numerical integration of oscillatory problems
Applied Numerical Mathematics
Trigonometrically-fitted ARKN methods for perturbed oscillators
Applied Numerical Mathematics
A robust trigonometrically fitted embedded pair for perturbed oscillators
Journal of Computational and Applied Mathematics
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A new embedded pair of explicit RKN methods adapted to the numerical integration of general perturbed oscillators is derived. This pair is based on the RKN methods adapted to the numerical integration of perturbed oscillators constructed by Franco (see Ref. [J.M. Franco, Runge-Kutta-Nystrom methods adapted to the numerical integration of perturbed oscillators, Comput. Phys. Commun. 147 (2002) 770-787]). It not only can be used to deal with the particular problems in which the perturbed functions are independent of y^' but the general problems. We show that the embedded methods have algebraic order 4 and 3. The numerical experiments show the efficiency of our pair compared with the variable step code proposed by Vanden Berghe et al. (see Ref. [G. Vanden Berghe, H. De Meyer, M. Van Daele, T. Van Hecke, Exponentially-fitted explicit Runge-Kutta methods, J. Comput. Appl. Math. 125 (2000) 107-115]) and the other high order Runge-Kutta(Nystrom) pairs (such as the Runge-Kutta 8(7) and 5(4) pair of Dormand and Prince given in Ref. [E. Hairer, S.P. Norsett, S.P. Wanner, Solving Ordinary Differential Equations I, Nonstiff Problems, Springer, Berlin, 1993]), when they are used to deal with the special problems with the perturbed functions independent of y^' as well as the general problems.