The BiM code for the numerical solution of ODEs. In this paper we present the code BiM, based on blended implicit methods (J. Comput. Appl. Math. 116 (2000) 41; Appl. Numer. Math. 42 (2002) 29; Recent Trends in Numerical Analysis, Nova Science Publ. Inc., New York, 2001, pp. 81.), for the numerical solution of stiff initial value problems for ODEs. We describe in detail most of the implementation strategies used in the construction of the code, and report numerical tests comparing the code BiM with some of the best codes currently available. The numerical tests show that the new code compares well with existing ones. Moreover, the methods implemented in the code are characterized by a diagonal nonlinear splitting, which makes its extension for parallel computers very straightforward.

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  1. Amodio, Pierluigi; Brugnano, Luigi; Iavernaro, Felice: Analysis of spectral Hamiltonian boundary value methods (SHBVMs) for the numerical solution of ODE problems (2020)
  2. Barletti, Luigi; Brugnano, Luigi; Tang, Yifa; Zhu, Beibei: Spectrally accurate space-time solution of Manakov systems (2020)
  3. Brugnano, Luigi; Iavernaro, Felice; Zhang, Ruili: Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles (2020)
  4. Brugnano, Luigi; Gurioli, Gianmarco; Sun, Yajuan: Energy-conserving Hamiltonian boundary value methods for the numerical solution of the Korteweg-de Vries equation (2019)
  5. Brugnano, Luigi; Montijano, Juan I.; Rández, Luis: On the effectiveness of spectral methods for the numerical solution of multi-frequency highly oscillatory Hamiltonian problems (2019)
  6. Barletti, L.; Brugnano, L.; Frasca Caccia, G.; Iavernaro, F.: Energy-conserving methods for the nonlinear Schrödinger equation (2018)
  7. Brugnano, Luigi; Gurioli, Gianmarco; Iavernaro, Felice; Weinmüller, Ewa B.: Line integral solution of Hamiltonian systems with holonomic constraints (2018)
  8. Brugnano, Luigi; Iavernaro, Felice: Line integral solution of differential problems (2018)
  9. Wang, Bin; Meng, Fanwei; Fang, Yonglei: Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations (2017)
  10. Brugnano, L.; Frasca Caccia, G.; Iavernaro, F.: Energy conservation issues in the numerical solution of the semilinear wave equation (2015)
  11. Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia: Efficient implementation of Radau collocation methods (2015)
  12. Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice: Efficient implementation of Gauss collocation and Hamiltonian boundary value methods (2014)
  13. Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline: A test set for stiff initial value problem solvers in the open source software R: Package \textbfdeTestSet (2012)
  14. Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato: A note on the efficient implementation of Hamiltonian BVMs (2011)
  15. Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato: Numerical solution of ODEs and the Columbus’ egg: three simple ideas for three difficult problems (2010)
  16. Brugnano, Luigi; Magherini, Cecilia: Recent advances in linear analysis of convergence for splittings for solving ODE problems (2009)
  17. Brugnano, Luigi; Magherini, Cecilia: Blended implicit methods for solving ODE and DAE problems, and their extension for second-order problems (2007)
  18. Brugnano, Luigi; Magherini, Cecilia: Economical error estimates for block implicit methods for ODEs via deferred correction. (2006)
  19. Brugnano, Luigi; Magherini, Cecilia; Mugnai, Filippo: Blended implicit methods for the numerical solution of DAE problems (2006)
  20. Brugnano, Luigi; Magherini, Cecilia: Some linear algebra issues concerning the implementation of blended implicit methods. (2005)

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