Abstract
We discuss a number of different methods for second order differential systems \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} '' = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{F} \left( {t, \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} } \right)\) each of which reduce to two-step methods for linear homogeneous systems \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} '' + K\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{x} = \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{g} \left( t \right)\). It is shown that some apparently unconnected methods are closely related when applied to this simple problem.
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© 1984 Springer-Verlag
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Gladwell, I., Thomas, R.M. (1984). A-stable methods for second order differential systems and their relation to Padé approximants. In: Graves-Morris, P.R., Saff, E.B., Varga, R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072429
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DOI: https://doi.org/10.1007/BFb0072429
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