Overdetermined least-squares collocation for higher-index differential-algebraic equations
Roswitha März (Institut für Mathematik, Humboldt-Universität zu Berlin)
R 3.28 Mon Z2 17:30-17:55
This is again a joint effort with Michael Hanke (KTH Stockholm) and ties in with the results we both presented at NUMDIFF-15.
We are looking for an approximate solution of the initial- or boundary-value problem The DAE in it can be of arbitrarily high index. The ansatz-space consists of componentwise and piecewise polynomial functions on the grid , with continuously connected part . We use polynomials of degree for the component but for the nondifferentiated part degree . Introducing so-called collocation nodes and in turn , we form the overdetermined collocation system which is then solved into a special least-squares sense for . The procedure is inherently simple, the numerical tests are surprisingly good, but the underlying theory is quite demanding. Considering the fact that we are dealing here with an essentially ill-posed problem, it is important to implement it very carefully. Many questions are still open. We describe achievements, difficulties and surprises.
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