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Bounds for the error in approximate solutions of ordinary differential equations

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Conference on Applications of Numerical Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 228))

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Abstract

The article outlines the derivation of error bounds for numerical solutions of initial value problems for ordinary differential equations. These bounds depend on a bound for the norm of the fundamental matrix of a linear system and on a bound for the norm of the approximation defect. Error bounds are usually expressed as the solution of a linear differential equation but may also be obtained as the solution of a Riccati equation.

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References

  1. Bonsall, F.F. and J. Duncan; Numerical Ranges of Operators on Normed Spaces and of Elements of Normed Algebras, London Math. Soc., Lecture Note Series 2, C.U.P. (1971).

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  5. Lakshmikanthan, V. and S. Leela, Differential and Integral Inequalities, Vol. 1., pp. 315–322. Academic Press, New York (1969).

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  7. Sansone, G. and R. Conti, Nonlinear Differential Equations (revised ed.), pp. 10–15. Pergamon Press, Oxford (1964).

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Authors
  1. G. J. Cooper
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John Ll. Morris

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© 1971 Springer-Verlag

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Cooper, G.J. (1971). Bounds for the error in approximate solutions of ordinary differential equations. In: Morris, J.L. (eds) Conference on Applications of Numerical Analysis. Lecture Notes in Mathematics, vol 228. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069461

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  • DOI: https://doi.org/10.1007/BFb0069461

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05656-0

  • Online ISBN: 978-3-540-36976-9

  • eBook Packages: Springer Book Archive

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