130 citations · 506 across the 27 of their papers we have counts for
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New integration methods for perturbed ODEs based on symplectic implicit Runge-Kutta schemes with application to solar system simulations
Mikel Antoñana, Joseba Makazaga, Ander Murua
We propose a family of integrators, Flow-Composed Implicit Runge-Kutta (FCIRK) methods, for perturbations of nonlinear ordinary differential equations, consisting of the compositio…
Efficient implementation of symplectic implicit Runge-Kutta schemes with simplified Newton iterations
Mikel Antoñana, Joseba Makazaga, Ander Murua
We are concerned with the efficient implementation of symplectic implicit Runge-Kutta (IRK) methods applied to systems of (non-necessarily Hamiltonian) ordinary differential equati…
Reducing and monitoring round-off error propagation for symplectic implicit Runge-Kutta schemes
Mikel Antoñana, Joseba Makazaga, Ander Murua
We propose an implementation of symplectic implicit Runge-Kutta schemes for highly accurate numerical integration of non-stiff Hamiltonian systems based on fixed point iteration. P…