An Interval Hermite-Obreschkoff Method for Computing Rigorous Bounds on the Solution of an Initial Value Problem for an Ordinary Differential Equation

Author:

Nedialkov Nedialko S.,Jackson Kenneth R.

Publisher

Springer Netherlands

Reference35 articles.

1. Adams, E., Cordes, D., and Lohner, R.: Enclosure of Solutions of Ordinary Initial Value Problems and Applications, in: Adams, E., Ansorge, R., Großmann, Ch., and Roos, H. G. (eds), Discretization in Differential Equations and Enclosures, Akademie-Verlag, Berlin, 1987, pp. 9–28.

2. Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.

3. Bendsten, C. and Stauning, O.: FADBAD, a Flexible C++ Package for Automatic Differentiation Using the Forward and Backward Methods,Technical Report 1996-x5–94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark, 1996. FADBAD is available at http://www.inun.dtu.dk/fadbad.html .

4. Bendsten, C. and Stauning, O.: TADIFF, a Flexible C++ Package for Automatic Differentiation Using Taylor Series,Technical Report 1997-x5–94, Department of Mathematical Modelling, Technical University of Denmark, DK-2800, Lyngby, Denmark, 1997. TADIFF is available at http://www.imm.dtu.dk/fadbad.html .

5. Birkhoff, G. and Varga, R. S.: Discretization Errors for Well-Set Cauchy Problems: I, J. Math. and Phys. 44 (1965), pp. 1–23.

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