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
Mixed collocation methods for y′′=fx,y
Journal of Computational and Applied Mathematics
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
Frequency determination and step-length control for exponentially-fitted Runge---Kutta methods
Journal of Computational and Applied Mathematics
Exponential fitted Runge--Kutta methods of collocation type: fixed or variable knot points?
Journal of Computational and Applied Mathematics
Geometric numerical integration by means of exponentially-fitted methods
Applied Numerical Mathematics
Symplectic conditions for exponential fitting Runge-Kutta-Nyström methods
Mathematical and Computer Modelling: An International Journal
Sixth-order symmetric and symplectic exponentially fitted Runge-Kutta methods of the Gauss type
Journal of Computational and Applied Mathematics
Trigonometric polynomial or exponential fitting approach?
Journal of Computational and Applied Mathematics
New embedded explicit pairs of exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
Symplectic exponentially-fitted four-stage Runge---Kutta methods of the Gauss type
Numerical Algorithms
Numerical stroboscopic averaging for ODEs and DAEs
Applied Numerical Mathematics
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The preservation of some structure properties of the flow of differential systems by numerical exponentially fitted Runge-Kutta (EFRK) methods is considered. A complete characterisation of EFRK methods that preserve linear or quadratic invariants is given and, following the approach of Bochev and Scovel [On quadratic invariants and symplectic structure, BIT 34 (1994) 337-345], the sufficient conditions on symplecticity of EFRK methods derived by Van de Vyver [A fourth-order symplectic exponentially fitted integrator, Comput. Phys. Comm. 174 (2006) 255-262] are obtained. Further, a family of symplectic EFRK two-stage methods with order four has been derived. It includes the symplectic EFRK method proposed by Van de Vyver as well as a collocation method at variable nodes that can be considered as the natural collocation extension of the classical RK Gauss method. Finally, the results of some numerical experiments are presented to compare the relative merits of several fitted and nonfitted fourth-order methods in the integration of oscillatory systems.