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Integral Treatment of O.D.E with Splines

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Constructive Methods for the Practical Treatment of Integral Equations

Part of the book series: International Series of Numerical Mathematics ((ISNM,volume 73))

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Abstract

A spline approximation for the initial value problem y’=f(x,y) was obtained by F.R. LOSCALZO and T.D. TALBOT [5],[6]. Then, following the method of LOSCALZO and TALBOT, G. MICULA, [7] presented a spline method for approximating the solution of y’=f(x,y) with y’ abscent. Recently, TH. FAWZY.[1]–[4] introduced several local spline methods, using g splines and non-polynomial splines, for approximating the solution of some initial value problems.

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References

  1. Fawzy, Th. Spline Functions and Cauchy Problems, I,III. Annales Univ. Sci. Budapest. Sec.Comp. Tom I. (1978), 81–98,

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  2. Fawzy, Th. Spline Functions and Cauchy Problems, I,III. Annales Univ. Sci. Budapest. Sec.Comp. Tom I. (1978), 35–46

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  5. Fawzy, Th. and A. Al-Mutib. Error of an arbitrary order for the approximate solution of y’=f(x,y) with spline functions. Proceeding of BAIL I Conference, Dublin 1980.

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  6. Fawzy, Th. Spline Functions and Cauchy Problems, VII. Annales Univ. Sci. Budapest Sec. Math. Tom 24 (1981), 57–62.

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  7. Loscalzo, F.R. and Talbot, T.D. Spline function approximation for solutions of ordinary diff. equations. Siam J. Num. Anal. 3, (1967), 433–445.

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  8. Loscalzo, F.R. and Talbot, T.D. Spline function approximation for solution of ordinary diff. equations. Bull. Am. Math. Soc. 73 (1967), 438–442

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  9. Micula, Gh. Approximate solution of the differential equation y’=f(x,y) with spline functions. Math, of Computation. Vol 27 No. 4 (1973). 807–816.

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Author information

Authors and Affiliations

  1. Math. Dept., Faculty of Science, Suez-Canal University, Ismailia, Egypt

    Tharwat Fawzy

Authors
  1. Tharwat Fawzy
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Editor information

Editors and Affiliations

  1. Mathematisches Institut der, Ludwig-Maximilians-Universität, Theresienstraße 39, D-8000, München 2, Germany

    G. Hämmerlin

  2. Mathematisches Institut, der Universität Augsburg, Memminger Straße 6, D-8900, Augsburg, Germany

    K.-H. Hoffmann

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© 1985 Birkhäuser Verlag Basel

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Fawzy, T. (1985). Integral Treatment of O.D.E with Splines. In: Hämmerlin, G., Hoffmann, KH. (eds) Constructive Methods for the Practical Treatment of Integral Equations. International Series of Numerical Mathematics, vol 73. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9317-6_12

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  • DOI: https://doi.org/10.1007/978-3-0348-9317-6_12

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9993-2

  • Online ISBN: 978-3-0348-9317-6

  • eBook Packages: Springer Book Archive

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