The Fortran 77 codes BiM and BiMD are based on blended implicit methods, namely a class of L-stable Block Implicit Methods providing a (relatively) easy definition of suitable nonlinear splittings for solving the corresponding discrete problems, [41,43,46,54]. In particular: the code BiM (release 2.0, April 2005) implements a variable order-variable stepsize method for (stiff) initial value problems for ODEs. The order of the method varies from 4 to 12, according to a suitable order variation strategy. All the details concerning the strategies implemented in the code BiM are described in [47,48,53] (see also Cecilia Magherini’s PhD thesis, also available as a compressed file); the code BiMD (release 1.1.2, November 2014) is a generalization of the code BiM for solving (stiff) initial value problems for linearly implicit DAEs of index up to 3 with constant mass matrix [54], namely problems in the form M y’ = f(t,y), where M is a constant, possibly singular, matrix.

References in zbMATH (referenced in 23 articles )

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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. Brugnano, Luigi; Zhang, Chengjian; Li, Dongfang: A class of energy-conserving Hamiltonian boundary value methods for nonlinear Schrödinger equation with wave operator (2018)
  10. Wang, Bin; Meng, Fanwei; Fang, Yonglei: Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations (2017)
  11. Benhammouda, Brahim; Vazquez-Leal, Hector: Analytical solution of a nonlinear index-three DAEs system modelling a slider-Crank mechanism (2015)
  12. Brugnano, L.; Frasca Caccia, G.; Iavernaro, F.: Energy conservation issues in the numerical solution of the semilinear wave equation (2015)
  13. Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia: Efficient implementation of Radau collocation methods (2015)
  14. Skvortsov, L. M.: A fifth order implicit method for the numerical solution of differential-algebraic equations (2015)
  15. Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice: Efficient implementation of Gauss collocation and Hamiltonian boundary value methods (2014)
  16. Skvortsov, L. M.; Kozlov, O. S.: Efficient implementation of diagonally implicit Runge-Kutta methods (2014)
  17. 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)
  18. Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato: A note on the efficient implementation of Hamiltonian BVMs (2011)
  19. Brugnano, Luigi; Magherini, Cecilia: Recent advances in linear analysis of convergence for splittings for solving ODE problems (2009)
  20. Brugnano, Luigi; Magherini, Cecilia: Blended implicit methods for solving ODE and DAE problems, and their extension for second-order problems (2007)

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