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In this paper we develop a technique for avoiding the order reduction caused by nonconstant boundary conditions in the methods called splitting , alternating direction or, more generally, fractional step methods. Such methods can be viewed as the combination of a semidiscrete in time procedure with a special type of additive Runge–Kutta method, which is… (More)

Two model problems for stii oscillatory systems are introduced. Both comprise a linear superposition of N 1 harmonic oscillators used as a forcing term for a scalar ODE. In the rst case the initial conditions are chosen so that the forcing term approximates a delta function as N ! 1 and in the second case so that it approximates white noise. In both cases… (More)

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… (More)

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 step-sizes and the variable coefficients. Then we prove asymptotic expansions on the considered tolerance for the global error committed. Using… (More)

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