Andrea Walther
Institute of Scientific Computing
Technical University Dresden, Germany
email: awalther@math.tu-dresden.de
and
Andreas Griewank
Institute of Mathematics
Humboldt University Berlin, Germany
email: awalther@math.tu-dresden.de
The application of Taylor methods for the integration of high-index DAEs requires the calculation of high-order derivatives. To compute the required information to any order one may use the technique of Automatic Differentiation (AD) in combination with Taylor arithmetic. Then, the complexity of the derivative calculations grows only quadratically in the highest order of the derivative. Here, we present the specific requirements with respect to the calculation of high order derivative when applied for the integration of DAEs. We use an integration method proposed by John Pryce [1] in combination with the high order derivatives provided by ADOL-C [2] for solving high-index DAEs. Numerical results verifying the approach are shown. Finally, we discuss an technique to reduce the cost caused by the calculation of high order derivatives even further.
References:
1. J. Pryce: Solving high-index DAEs by Taylor series. Numer. Algorithms 19, No.1-4, 195-211 (1998).
2. A. Griewank, D. Juedes, and J. Utke: ADOL-C: A package
for the automatic differentiation of algorithms written in C/C++. ACM Trans.
Math. Software 22, 131-167 (1996)