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
An embedded pair of exponentially fitted explicit 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
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
Structure preservation of exponentially fitted Runge-Kutta methods
Journal of Computational and Applied Mathematics
Trigonometric polynomial or exponential fitting approach?
Journal of Computational and Applied Mathematics
Symplectic exponentially-fitted four-stage Runge---Kutta methods of the Gauss type
Numerical Algorithms
Local path fitting: A new approach to variational integrators
Journal of Computational and Applied Mathematics
Exponentially fitted singly diagonally implicit Runge-Kutta methods
Journal of Computational and Applied Mathematics
Hi-index | 7.29 |
The construction of exponentially fitted Runge-Kutta (EFRK) methods for the numerical integration of Hamiltonian systems with oscillatory solutions is considered. Based on the symplecticness, symmetry, and exponential fitting properties, two new three-stage RK integrators of the Gauss type with fixed or variable nodes, are obtained. The new exponentially fitted RK Gauss type methods integrate exactly differential systems whose solutions can be expressed as linear combinations of the set of functions {exp(@lt),exp(-@lt)}, @l@?C, and in particular {sin(@wt),cos(@wt)} when @l=i@w, @w@?R. The algebraic order of the new integrators is also analyzed, obtaining that they are of sixth-order like the classical three-stage RK Gauss method. Some numerical experiments show that the new methods are more efficient than the symplectic RK Gauss methods (either standard or else exponentially fitted) proposed in the scientific literature.