Article ID Journal Published Year Pages File Type
4638959 Journal of Computational and Applied Mathematics 2014 11 Pages PDF
Abstract

Automatic (or Algorithmic) Differentiation (AD) opens new possibilities to analyze and solve DAEs by projector based methods. In this paper, we present a new approach to compute consistent initial values and integrate DAEs up to index two, considering the nonlinear DAE in each time-step as a nonlinear system of equations for Taylor expansions. These systems will be solved by the Newton–Kantorowitsch method, whereas the resulting linear systems are decoupled using the splitting techniques related to the tractability index concept. This approach provides a description of the inherent ODE that allows an application of the classical Taylor series method to the integration of initial value problems. Linear and nonlinear DAEs with index up to two are examined and solved numerically.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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