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

  • I. Gladwell
  • 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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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • I. Gladwell
    • 1
  • R. M. Thomas
    • 2
  1. 1.Department of MathematicsUniversity of ManchesterManchesterUK
  2. 2.Department of MathematicsU.M.I.S.T.ManchesterUK

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