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Computation of consistent initial values for properly stated index 3 DAEs. (English) Zbl 1162.65376

Summary: The computation of consistent initial values is one of the basic problems when solving initial or boundary value problems of differential-algebraic equations (DAEs). For a given DAE it is, in fact, not obvious how to formulate the initial conditions that lead to a uniquely solvable initial value problem (IVP). The existing algorithms for the solution of this problem are either designed for fixed index, or they require a special structure of the DAE or they need more than the given data (e.g. additional differentiations).
In this paper, combining the results concerning the solvability of DAEs with properly stated leading terms with an appropriate method for the approximation of the derivative, we propose an algorithm that provides the necessary data to formulate the initial conditions and which works at least for nonlinear DAEs up to index 3. Illustrative examples are given.

MSC:

65L80 Numerical methods for differential-algebraic equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations

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