Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Accurate long-term integration of dynamical systems
NUMDIFF-7 Selected papers of the seventh conference on Numerical treatment of differential equations
A generalization to variable stepsizes of Sto¨rmer methods for second-order differential equations
Applied Numerical Mathematics
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
Variable step implementation of geometric integrators
Applied Numerical Mathematics
Backward Error Analysis for Numerical Integrators
SIAM Journal on Numerical Analysis
Mathematics of Computation
Mathematics of Computation
Error propagation in numerical approximations near relative equilibria
Journal of Computational and Applied Mathematics
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In this paper we deal with several issues concerning variable-stepsize linear multistep methods. First, we prove their stability when their fixed-stepsize counterparts are stable and under mild conditions on the stepsizes and the variable coefficients. Then we prove asymptotic expansions on the considered tolerance for the global error committed. Using them, we study the growth of error with time when integrating periodic orbits. We consider strongly and weakly stable linear multistep methods for the integration of first-order differential systems as well as those designed to integrate special second-order ones. We place special emphasis on the latter which are also symmetric because of their suitability when integrating moderately eccentric orbits of reversible systems. For these types of methods, we give a characterization for symmetry of the coefficients, which allows their construction, and provide some numerical results for them.