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Error bounds for some single step methods

Part of the Lecture Notes in Mathematics book series (LNM,volume 109)

Abstract

The truncation error in single step methods for ordinary differential equations may be bounded by terms which represent quadrature remainders. The remainders may be determined by applying Peano's theorem and this treatment suggests a variety of methods based on quadrature rules. In some cases the error bounds improve on classical results.

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References

  1. Butcher, J. C.: "On the Convergence of Numerical Solutions to Ordinary Differential Equations". J. Maths. Comp., v.20, 1966, pp. 1–10.

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© 1969 Springer-Verlag

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Cooper, G.J. (1969). Error bounds for some single step methods. In: Morris, J.L. (eds) Conference on the Numerical Solution of Differential Equations. Lecture Notes in Mathematics, vol 109. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060020

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  • DOI: https://doi.org/10.1007/BFb0060020

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04628-8

  • Online ISBN: 978-3-540-36158-9

  • eBook Packages: Springer Book Archive