Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
The parameterization method in optimal control problems and differential-algebraic equations
Journal of Computational and Applied Mathematics - Special issue: International workshop on the technological aspects of mathematics
The method of normal splines for linear DAEs on the number semi-axis
Applied Numerical Mathematics
The parameterization method in singular differential-algebraic equations
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
Development of the normal spline method for linear integro-differential equations
ICCS'03 Proceedings of the 2003 international conference on Computational science: PartII
The method of normal splines for linear DAEs on the number semi-axis
Applied Numerical Mathematics
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The paper explains the numerical parametrization method (PM), originally created for optimal control problems, for classical calculus of variation problems that arise in connection with singular implicit (IDEs) and differential-algebraic equations (DAEs) in frame of their regularization. The PM for IDEs is based on representation of the required solution as a spline with moving knots and on minimization of the discrepancy functional with respect to the spline parameters. Such splines are named variational splines. For DAEs only finite entering functions can be represented by splines, and the functional under minimization is the discrepancy of the algebraic subsystem. The first and the second derivatives of the functionals are calculated in two ways - for DAEs with the help of adjoint variables, and for IDE directly. The PM does not use the notion of differentiation index, and it is applicable to any singular equation having a solution.