This article is cited in 5 papers

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

M. V. Bulatov^a, N. P. Rahvalov^b, L. S. Solovarova<sup>a

a</sup> Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences, Irkutsk
^b East Siberian State Academy of Education, Irkutsk

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.

Key words: system of differential-algebraic equations, spline method, vector spline, index of a differential-algebraic equation.

UDC: 519.62

MSC: 34A09,65L80

Received: 06.04.2012
Revised: 10.10.2012

DOI: 10.7868/S0044466913030046

 English version: Computational Mathematics and Mathematical Physics, 2013, 53:3, 284–295

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