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Bounds of high quality for first kind Volterra integral equations

Тесные границы рещений интегральных уравнений Вольтерра первого рода

  • Mathematical Research
  • Published:
Reliable Computing

Abstract

E-Methods for solving linear Volterra integral equations of the first kind with smooth kernels are considered.E-Methods are a new type of numerical algorithms computing numerical approximations together with mathematically guaranteed close error bounds. The basic concepts from verification theory are sketched and such self-validating numerics derived. Computational experiments show the efficiency of these procedures being an advance in numerical methods.

Abstract

РассматриваютсяE-методы решения динейных интегральных уравнений Вольтерра первого рода с гладким ядром.E-методы представляют собой новый тип численных алгоритмов, позволяюяющих нолучить одновременно с численными приближениями математически гарантированные тесные гранипы погрешностей. В работе излагаются основные понятия теории верификации и ее прияожения в области самоверифицируюпщх вычислений. Численные эксперименты показывают эффективность этих новых вычислительных методов. mis© H.-J. Dobner, 1996

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References

  1. De Hoog, F. and Weiss, R.High order methods for Volterra integral equations of the first kind. SIAM J. Numer. Anal.10 (4) (1973), pp. 647–664.

    MathSciNet  Google Scholar 

  2. Delves, L. M. and Mohamed, J. L.Computational methods for integral equations. Cambridge University Press, Cambridge, 1985.

    Google Scholar 

  3. Dobner, H.-J. and Kaucher, E.Singular operator equations with functional constraints. In: Atanassova, L. and Herzberger, J. (eds) “Computer Arithmetic and Enclosure Methods”, Elsevier, 1992, pp. 235–241.

  4. Fenyö, S. and Stolle, H. W.Theorie und Praxis der linearen Integralgleichungen 4. Birkhäuser, Basel, Boston, Stuttgart, 1989.

    Google Scholar 

  5. Hadamard, J.Lectures on Cauchy's problem in linear partial differential equations. Yale University Press, New Haven, 1923.

    Google Scholar 

  6. Kaucher, E. and Baumhof, C.A verified computation of Fourier-representations of solutions for functional equations. Computing Suppl.9 (1993), pp. 101–115.

    Google Scholar 

  7. Kaucher, E. and Miranker, W. L.Self validating numerics for function space problems. Academic Press, New York, 1984.

    Google Scholar 

  8. Klatte, R., Kulisch, U., Neaga, M., Ratz, D., and Ullrich, C.PASCAL-XSC. Springer-Verlag, Berlin, Heidelberg, New York, 1991.

    Google Scholar 

  9. Kulisch, U. and Miranker, W. L.Computer arithmetic in theory and practice. Academic Press, New York, 1981.

    Google Scholar 

  10. Linz, P.Analytical and numerical methods for Volterra equations. SIAM, Philadelphia, 1985.

    Google Scholar 

  11. Moore, R. E.Interval analysis. Prentice Hall, Englewood Cliffs, N.J., 1966.

    Google Scholar 

  12. Rall, L.Automatic differentiation. Springer Lecture Notes in Computer Science 120, Berlin, Heidelberg, New York, 1981.

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Authors and Affiliations

  1. Mathematisches Institut II, Universität Karlsruhe, 76128, Karlsruhe, Germany

    Hans-Jürgen Dobner

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  1. Hans-Jürgen Dobner
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Dobner, HJ. Bounds of high quality for first kind Volterra integral equations. Reliable Comput 2, 35–45 (1996). https://doi.org/10.1007/BF02388186

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  • DOI: https://doi.org/10.1007/BF02388186

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