ATOMFT

ATOMFT: Solving ODEs and DAEs using Taylor series. The ATOMFT system, based on a Taylor series method, is designated to solve stiff and nonstiff initial value problems for ordinary differential and differential-algebraic equations. In the paper applications of this system to various problems are given.

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References in zbMATH (referenced in 42 articles , 1 standard article )

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  1. Amore, Paolo: Computing the solutions of the van der Pol equation to arbitrary precision (2022)
  2. Estévez Schwarz, Diana; Lamour, René: InitDAE: computation of consistent values, index determination and diagnosis of singularities of DAEs using automatic differentiation in Python (2021)
  3. Tariq, Hira; Günerhan, Hatıra; Rezazadeh, Hadi; Adel, Waleed: A numerical approach for the nonlinear temporal conformable fractional foam drainage equation (2021)
  4. Freihet, Asad; Hasan, Shatha; Al-Smadi, Mohammed; Gaith, Mohamed; Momani, Shaher: Construction of fractional power series solutions to fractional stiff system using residual functions algorithm (2019)
  5. Schaumburg, Herman D.; Al Marzouk, Afnan; Erdelyi, Bela: Picard iteration-based variable-order integrator with dense output employing algorithmic differentiation (2019)
  6. Al Khawaja, U.; Al-Mdallal, Qasem M.: Convergent power series of (\operatornamesech(x)) and solutions to nonlinear differential equations (2018)
  7. 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)
  8. Marzouk, Afnan Al; Erdelyi, Bela: Collisional (N)-body numerical integrator with applications to charged particle dynamics (2018)
  9. Abad, A.; Barrio, R.; Marco-Buzunariz, M.; Rodríguez, M.: Automatic implementation of the numerical Taylor series method: a \textscMathematicaand \textscSageapproach (2015)
  10. El-Ajou, Ahmad; Abu Arqub, Omar; Al-Smadi, Mohammed: A general form of the generalized Taylor’s formula with some applications (2015)
  11. Estévez Schwarz, Diana; Lamour, René: Projector based integration of DAEs with the Taylor series method using automatic differentiation (2014)
  12. Shokri, Ali: One and two-step new hybrid methods for the numerical solution of first order initial value problems (2014)
  13. Banerjee, Joydeep M.; McPhee, John: Symbolic sensitivity analysis of multibody systems (2013)
  14. Abad, Alberto; Barrio, Roberto; Blesa, Fernando; Rodríguez, Marcos: Algorithm 924, TIDES, a Taylor series integrator for differential equations (2012)
  15. Bervillier, C.: Status of the differential transformation method (2012)
  16. Rodríguez, Marcos; Barrio, Roberto: Reducing rounding errors and achieving Brouwer’s law with Taylor series method (2012)
  17. Thelwell, Roger J.; Warne, Paul G.; Warne, Debra A.: Cauchy-Kowalevski and polynomial ordinary differential equations (2012)
  18. Barrio, R.; Rodríguez, M.; Abad, A.; Blesa, F.: Breaking the limits: The Taylor series method (2011)
  19. Barrio, R.; Rodríguez, M.; Abad, A.; Serrano, S.: Uncertainty propagation or box propagation (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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