Solving differential algebraic equations by Taylor Series(III): the DAETS Code

Abstract

The authors have developed a Taylor series method for solving numerically an initial-value problem differential algebraic equation (DAE) that can be of high index, high order, nonlinear, and fully implicit, see BIT 45:561{592, 2005 and BIT 41:364-394, 2001. Numerical results have shown this method to be efficient and very accurate, and particularly suitable for problems that are of too high an index for present DAE solvers. This paper outlines this theory and describes the design, implementation, usage and performance of Daets, a DAE solver based on this theory and written in C++.