Numerical solution of differential-algebraic equations using the spline collocation-variation method. (Russian, English) Zbl 1274.65228
Zh. Vychisl. Mat. Mat. Fiz. 53, No. 3, 377-389 (2013); translation in Comput. Math. Math. Phys. 53, No. 3, 284-295 (2013).
Summary: Numerical methods for solving initial value problems of 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.
MSC:
| 65L80 | Numerical methods for differential-algebraic equations |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
Keywords:
differential-algebraic equations; spline collocation-variation method; continuous vector spline; index of differential-algebraic equationsSoftware:
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