Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The development of variable-step symplectic integrators with application to the two-body problem
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Reversible Long-Term Integration with Variable Stepsizes
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Variable time step integration with symplectic methods
Applied Numerical Mathematics - Special issue on time integration
Construction of starting algorithms for the RK-Gauss methods
Journal of Computational and Applied Mathematics
Variable step implementation of geometric integrators
Applied Numerical Mathematics
Backward Error Analysis for Numerical Integrators
SIAM Journal on Numerical Analysis
Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones
Mathematics of Computation
Analysis of variable-stepsize linear multistep methods with special emphasis on symmetric ones
Mathematics of Computation
Error propagation in numerical approximations near relative equilibria
Journal of Computational and Applied Mathematics
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Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.