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Erschienen in:
2010 | OriginalPaper | Buchkapitel
Linear Multistep Methods—I: Construction and Consistency
verfasst von : David F. Griffiths, Desmond J. Higham
Erschienen in: Numerical Methods for Ordinary Differential Equations
Verlag: Springer London
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The effectiveness of the family of TS(
p
) methods has been evident in the preceding chapter. For order
p
> 1, however, they suffer a serious disadvantage in that they require the right-hand side of the differential equation to be differentiated a number of times. This often rules out their use in real-world applications, which generally involve (large) systems of ODEs whose differentiation is impractical unless automated tools are used [23]. We look, therefore, for alternatives that do not require the use of second and higher derivatives of the solution.