Solving high-index DAEs by Taylor series
We present a general method of solving differential-algebraic equations by expanding the solution as a Taylor series. It seems especially suitable for (piecewise) smooth problems of high index. We describe the method in general, discuss steps to be taken if the method, as initially applied, fails because it leads to a system of equations with identically singular Jacobian, and illustrate by solving two problems of index 5.
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