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Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations. I: Basics and ansatz function choices. (English) Zbl 1484.65164

Summary: In the two parts of the present note we discuss several questions concerning the implementation of overdetermined least-squares collocation methods for higher index differential-algebraic equations (DAEs). Since higher index DAEs lead to ill-posed problems in natural settings, the discrete counterparts are expected to be very sensitive, which attaches particular importance to their implementation. In the present Part 1, we provide a robust selection of basis functions and collocation points to design the discrete problem. We substantiate a procedure for its numerical solution later in Part 2 [the authors, ibid. 89, No. 3, 965–986 (2022; Zbl 1484.65165)]. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.

MSC:

65L80 Numerical methods for differential-algebraic equations
65L08 Numerical solution of ill-posed problems involving ordinary differential equations
65F20 Numerical solutions to overdetermined systems, pseudoinverses
34A99 General theory for ordinary differential equations

Citations:

Zbl 1484.65165
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