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

Authors:
M. V. Bulatov;N. P. Rakhvalov;L. S. Solovarova
Affiliations:
Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia 664033;Irkutsk State Pedagogical University, Irkutsk, Russia 664011;Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, Irkutsk, Russia 664033
Venue:
Computational Mathematics and Mathematical Physics
Year:
2013

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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.