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On the equivalence of the continuous Adams-Bashforth method and Nordsieck’s technique for changing the step size. (English) Zbl 1308.65120
Summary: Recent research has raised the question of whether Nordsieck’s technique for changing the step size in the Adams-Bashforth method is equivalent to the explicit continuous Adams-Bashforth method. This work provides a complete proof that the two approaches are indeed equivalent.

MSC:
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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[1] Berardi, M.; Lopez, L., On the continuous extension of Adams-bashforth methods and the event location in discontinuous odes, Applied Mathematics Letters, 25, 995-999, (2012) · Zbl 1242.65128
[2] Lambert, J. D., Numerical methods for ordinary differential systems: the initial value problem, (1991), John Wiley London · Zbl 0745.65049
[3] Nordsieck, A., On numerical integration of ordinary differential equations, Mathematics of Computation, 16, 22-49, (1962) · Zbl 0105.31902
[4] Hairer, E.; Norsett, P. S.; Wanner, G., Solving ordinary differential equation I: nonstiff problems, (2008), Springer-Verlag Berlin
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