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- Manuel Calvo, J. M. Franco, Juan I. Montijano, Luis Rández
- Computer Physics Communications
- 2008

- J. M. Franco, I. Gómez, Luis Rández
- Numerical Algorithms
- 2001

New SDIRKN methods specially adapted to the numerical integration of second-order stiff ODE systems with periodic solutions are obtained. Our interest is focused on the dispersion (phase errors) of the dominant components in the numerical oscillations when these methods are applied to the homogeneous linear test model. Based on this homogeneous test model… (More)

- M. CALVO, D. J. HIGHAM, L. RANDEZ
- 1996

Users of locally-adaptive software for initial value ordinary differential equations are likely to be concerned with global errors. At the cost of extra computation, global error estimation is possible. Zadunaisky's method and 'solving for the error estimate' are two techniques that have been successfully incorporated into Runge-Kutta algorithms. The… (More)

- Manuel Calvo, D. Hernández-Abreu, Juan I. Montijano, Luis Rández
- SIAM J. Scientific Computing
- 2006

- Manuel Calvo, Desmond J. Higham, Juan I. Montijano, Luis Rández
- Adv. Comput. Math.
- 1997

The potential for adaptive explicit Runge–Kutta (ERK) codes to produce global errors that decrease linearly as a function of the error tolerance is studied. It is shown that this desirable property may not hold, in general, if the leading term of the locally computed error estimate passes through zero. However, it is also shown that certain methods are… (More)

- Manuel Calvo, M. P. Laburta, Juan I. Montijano, Luis Rández
- Mathematics and Computers in Simulation
- 2011

- Manuel Calvo, Laurent O. Jay, Juan I. Montijano, Luis Rández
- Numerische Mathematik
- 2004

The so-called multi-revolution methods were introduced in celestial mechanics as an efficient tool for the long-term numerical integration of nearly periodic orbits of artificial satellites around the Earth. A multi-revolution method is an algorithm that approximates the map φNT of N near-periods T in terms of the one near-period map φT evaluated at few s ≪… (More)

- M. P. Laburta, Juan I. Montijano, Luis Rández, Manuel Calvo
- Computer Physics Communications
- 2015

- Luigi Brugnano, Manuel Calvo, Juan I. Montijano, Luis Rández
- J. Computational Applied Mathematics
- 2012

<lb>We present and analyze energy-conserving methods for the numerical inte-<lb>gration of IVPs of Poisson type systems that are able to preserve some Casimirs.<lb>Their derivation and analysis is done within the framework following the ideas<lb>of Hamiltonian BVMs (HBVMs) (see [1] and references therein). The pro-<lb>posed methods turn out to be equivalent… (More)

- Manuel Calvo, Juan I. Montijano, Luis Rández
- Numerical Algorithms
- 2003

In this paper an automatic technique for handling discontinuous IVPs when they are solved by means of adaptive Runge–Kutta codes is proposed. This technique detects, accurately locates and passes the discontinuities in the solution of IVPs by using the information generated by the code along the numerical integration together with a continuous interpolant… (More)