An Hermite-Obreschkoff method for stiff high-index DAE

We have developed an implicit Hermite-Obreschkoff method for the numerical solution of stiff high-index differential-algebraic equations (DAEs). On each integration step, this method requires the computation of Taylor coefficients and their gradients to construct and solve a nonlinear system for the numerical solution, which is then projected to satisfy the constraints of the problem. We derive this system, show how to compute its Jacobian …