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. Al Khawaja, U.; Al-Mdallal, Qasem M.: Convergent power series of (\operatornamesech(x)) and solutions to nonlinear differential equations (2018)
  2. Al Sakkaf, Laila Y.; Al-Mdallal, Qasem M.; Al Khawaja, U.: A numerical algorithm for solving higher-order nonlinear BVPs with an application on fluid flow over a shrinking permeable infinite long cylinder (2018)
  3. Estévez Schwarz, Diana; Lamour, René: A new approach for computing consistent initial values and Taylor coefficients for DAEs using projector-based constrained optimization (2018)
  4. Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning; Li, Xiao: How AD can help solve differential-algebraic equations (2018)
  5. McKenzie, Ross; Pryce, John: Structural analysis based dummy derivative selection for differential algebraic equations (2017)
  6. Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D.: Symbolic-numeric methods for improving structural analysis of differential-algebraic equation systems (2016)
  7. Nedialkov, Nedialko S.; Pryce, John D.; Tan, Guangning: Algorithm 948: DAESA -- a Matlab tool for structural analysis of differential-algebraic equations: software (2015)
  8. Pryce, J.; Nedialkov, N.; Tan, G.; McKenzie, R.: Exploiting block triangular form for solving DAEs: reducing the number of initial values (2015)
  9. Pryce, John D.; Nedialkov, Nedialko S.; Tan, Guangning: DAESA -- a Matlab tool for structural analysis of differential-algebraic equations: theory (2015)
  10. Tan, Guangning; Nedialkov, Nedialko S.; Pryce, John D.: A simple method for quasilinearity analysis of DAEs (2015)
  11. Estévez Schwarz, Diana; Lamour, René: Projector based integration of DAEs with the Taylor series method using automatic differentiation (2014)
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  15. Charpentier, I.: On higher-order differentiation in nonlinear mechanics (2012)
  16. Lamour, René; März, Roswitha: Detecting structures in differential algebraic equations: computational aspects (2012)
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  18. Konguetsof, A.: A hybrid method with phase-lag and derivatives equal to zero for the numerical integration of the Schrödinger equation (2011)
  19. Lamour, René; Monett, Dagmar: A new algorithm for index determination in DAEs using algorithmic differentiation (2011)
  20. 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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