Abstract
Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. Without advocating a particular solver we discuss how this information can be efficiently obtained using ADOL-C or similar automatic differentiation packages.
This work was supported by the DFG research center MATHEON, Mathematics for Key Technologies in Berlin, and DFG grant WA 1607/2-1.
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Griewank, A., Walther, A. (2006). On the Efficient Generation of Taylor Expansions for DAE Solutions by Automatic Differentiation. In: Dongarra, J., Madsen, K., Waśniewski, J. (eds) Applied Parallel Computing. State of the Art in Scientific Computing. PARA 2004. Lecture Notes in Computer Science, vol 3732. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11558958_131
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DOI: https://doi.org/10.1007/11558958_131
Publisher Name: Springer, Berlin, Heidelberg
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