Solving differential algebraic equations by Taylor series. III: The DAETs code. 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 part I, BIT 45, No. 3, 561--592 (2005; Zbl 1084.65075) and part II, BIT 41, 364--394 (2007; Zbl 1123.65080)]. 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++.

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  1. Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D.: Symbolic-numeric methods for improving structural analysis of differential-algebraic equation systems (2016)
  2. Pryce, J.; Nedialkov, N.; Tan, G.; McKenzie, R.: Exploiting block triangular form for solving DAEs: reducing the number of initial values (2015)
  3. Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning: DAESA -- a Matlab tool for structural analysis of differential-algebraic equations: theory (2015)
  4. Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D.: A simple method for quasilinearity analysis of DAEs (2015)
  5. Estévez Schwarz, Diana; Lamour, René: Projector based integration of DAEs with the Taylor series method using automatic differentiation (2014)
  6. Hasenauer, J.; Wolf, V.; Kazeroonian, A.; Theis, F.J.: Method of conditional moments (MCM) for the chemical master equation (2014)
  7. Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodríguez, Marcos: Algorithm 924, TIDES, a Taylor series integrator for differential equations (2012)
  8. Bervillier, C.: Status of the differential transformation method (2012)
  9. Charpentier, I.: On higher-order differentiation in nonlinear mechanics (2012)
  10. Lamour, René; März, Roswitha: Detecting structures in differential algebraic equations: computational aspects (2012)
  11. Barrio, R.; Rodríguez, M.; Abad, A.; Blesa, F.: Breaking the limits: The Taylor series method (2011)
  12. Konguetsof, A.: A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation (2011)
  13. Lamour, René; Monett, Dagmar: A new algorithm for index determination in DAEs using algorithmic differentiation (2011)
  14. Nguyen-Ba, Truong; Hao, Han; Yagoub, Hemza; Vaillancourt, Rémi: One-step 9-stage Hermite-Birkhoff-Taylor DAE solver of order 10 (2011)
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  16. Aschemann, H.; Minisini, J.; Rauh, A.: Interval arithmetic techniques for the design of controllers for nonlinear dynamical systems with applications in mechatronics. II (2010)
  17. Konguetsof, A.: Two-step high order hybrid explicit method for the numerical solution of the Schrödinger equation (2010)
  18. Konguetsof, A.: A new two-step hybrid method for the numerical solution of the Schrödinger equation (2010)
  19. Simos, T.E.: Exponentially and trigonometrically fitted methods for the solution of the Schrödinger equation (2010)
  20. Anastassi, Z.A.; Vlachos, D.S.; Simos, T.E.: A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems (2009)

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