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Date : |
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Place : |
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Lecturer: |
John Butcher
(University of Auckland)
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Title : |
Runge-Kutta methods for ordinary differential equations
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Abstract: |
Runge-Kutta methods are widely used in modern computation. This survey
will include a discussion of their order conditions and attempts to
construct methods which satisfy these conditions. An outline proof will
be given of the main order barrier (fifth order methods require more than
5 stages) and related results will be summarised. This will lead to a the
idea of effective order as a means of avoiding some of the consequences of
this barrier. For the solution of stiff problems, the use of implicit
methods is preferred and some of the important families of implicit
Runge-Kutta methods will be introduced.
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