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Numerical solution of differential-algebraic equations using the spline collocation-variation method

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Abstract

Numerical methods for solving initial value problems for differential-algebraic equations are proposed. The approximate solution is represented as a continuous vector spline whose coefficients are found using the collocation conditions stated for a subgrid with the number of collocation points less than the degree of the spline and the minimality condition for the norm of this spline in the corresponding spaces. Numerical results for some model problems are presented.

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Authors and Affiliations

  1. Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 134, Irkutsk, 664033, Russia

    M. V. Bulatov & L. S. Solovarova

  2. Irkutsk State Pedagogical University, Nizhnyaya Naberezhnaya 6, Irkutsk, 664011, Russia

    N. P. Rakhvalov

Authors
  1. M. V. Bulatov
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  2. N. P. Rakhvalov
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  3. L. S. Solovarova
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Correspondence to M. V. Bulatov.

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Original Russian Text © M.V. Bulatov, N.P. Rakhvalov, L.S. Solovarova, 2013, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2013, Vol. 53, No. 3, pp. 377–389.

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Bulatov, M.V., Rakhvalov, N.P. & Solovarova, L.S. Numerical solution of differential-algebraic equations using the spline collocation-variation method. Comput. Math. and Math. Phys. 53, 284–295 (2013). https://doi.org/10.1134/S0965542513030044

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  • DOI: https://doi.org/10.1134/S0965542513030044

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