Towards a reliable implementation of least-squares collocation for higher index differential-algebraic equations—Part 1: basics and ansatz function choices
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AbstractIn 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. Additionally, in Part 1, a number of new error estimates are proven that support some of the design decisions.
2019 ◽
pp. 112514
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2017 ◽
Vol 317
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pp. 403-431
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2014 ◽
Vol 259
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pp. 138-152
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2021 ◽
2020 ◽
Vol 149
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pp. 43-51
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1977 ◽
Vol 17
(4)
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pp. 3-16
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