Solving differential-algebraic equations by Taylor series. II: Computing the system Jacobian (Q878197)

In part I [BIT 45, 561--592 (2005; Zbl 1084.65075)] the authors have developed a Taylor series method for solving numerically an initial-value problem of an differential-algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit. In the present paper they develop an effective method for computing the Jacobian of a system of DAE's, which is needed in the structural analysis of the DAE and computation of Taylor coefficients. Theory and algorithms for preprocessing and code generation are presented. An operator-overloading approach to computing the system Jacobian is also discussed.