# A-stable methods for second order differential systems and their relation to Padé approximants

• R. M. Thomas
Numerical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

## 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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