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Advances in Applied Mathematics and Approximation Theory pp 165–181Cite as

To Approximate Solution of Ordinary Differential Equations, I

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Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 41))

Abstract

This article is dedicated to approximate solution of two-point boundary value problems for linear and nonlinear normal systems of ordinary differential equations. We study problems connected with solvability, construction of high order finite difference and finite sums schemes, error estimation and investigate the order of arithmetic operations for finding approximate solutions. Corresponding results refined and generalized well-known classical achievements in this field.

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Notes

  1. 1.

    Here, please note that the notation (x (k + 1)z + 1, 0) underlines that the corresponding Cauchy problem solved from the initial point x (k + 1)z + 1 to the point zero.

References

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  3. G. Strang, G. Fix, An Analysis of Finite Element Method, Wellesley-Cambridge, 1980 (second ed.).

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  4. T. Vashakmadze, Numerical Analysis, I, Tbilisi University Press, 2009 (in Georgian).

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  5. T. Vashakmadze, The Theory of Anisotropic Elastic Plates, Kluwer Acad. Publ&Springer. Dortrecht/Boston/ London, 2010 (second ed.).

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  6. T. Vashakmadze, To Approximate Solution of Ordinary Differential Equations, in International Conference on Appl.Mathematics and Approximate Theory (Abstract Book), Ankara, 2012, p102.

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Author information

Authors and Affiliations

  1. I.Vekua Institute of Applied Mathematics, Iv. Javakhishvili Tbilisi State University, Tbilisi, Georgia

    Tamaz S. Vashakmadze

Authors
  1. Tamaz S. Vashakmadze
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Correspondence to Tamaz S. Vashakmadze .

Editor information

Editors and Affiliations

  1. , Department of Mathematical Sciences, The University of Memphis, Memphis, 38152, Tennessee, USA

    George A. Anastassiou

  2. , Department of Mathematics, TOBB Economics and Technology University, Sögütözü, Ankara, 06530, Turkey

    Oktay Duman

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Vashakmadze, T.S. (2013). To Approximate Solution of Ordinary Differential Equations, I. In: Anastassiou, G., Duman, O. (eds) Advances in Applied Mathematics and Approximation Theory. Springer Proceedings in Mathematics & Statistics, vol 41. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6393-1_10

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