05146220

j

05146220 Nedialkov, Nedialko S. Pryce, John D. Solving differential-algebraic equations by Taylor series. II: Computing the system Jacobian. BIT 47, No. 1, 121-135 (2007). 2007 Springer, Dordrecht EN differential-algebraic equations(DAE) structural analysis Taylor series automatic differentiation algorithms Zbl 1084.65075

doi:10.1007/s10543-006-0106-8

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. R\u azvan R\u aducanu (Ia\c si)