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 13 articles )

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  1. Brugnano, Luigi; Gurioli, Gianmarco; Iavernaro, Felice; Weinmüller, Ewa B.: Line integral solution of Hamiltonian systems with holonomic constraints (2018)
  2. Wang, Bin; Meng, Fanwei; Fang, Yonglei: Efficient implementation of RKN-type Fourier collocation methods for second-order differential equations (2017)
  3. Brugnano, Luigi; Iavernaro, Felice; Magherini, Cecilia: Efficient implementation of Radau collocation methods (2015)
  4. Skvortsov, L.M.: A fifth order implicit method for the numerical solution of differential-algebraic equations (2015)
  5. Brugnano, Luigi; Caccia, Gianluca Frasca; Iavernaro, Felice: Efficient implementation of Gauss collocation and Hamiltonian boundary value methods (2014)
  6. Skvortsov, L.M.; Kozlov, O.S.: Efficient implementation of diagonally implicit Runge-Kutta methods (2014)
  7. Mazzia, Francesca; Cash, Jeff R.; Soetaert, Karline: A test set for stiff initial value problem solvers in the open source software R: Package \bfdeTestSet (2012)
  8. Brugnano, Luigi; Iavernaro, Felice; Trigiante, Donato: A note on the efficient implementation of Hamiltonian BVMs (2011)
  9. Brugnano, Luigi; Magherini, Cecilia: Recent advances in linear analysis of convergence for splittings for solving ODE problems (2009)
  10. Brugnano, Luigi; Magherini, Cecilia: Blended implicit methods for solving ODE and DAE problems, and their extension for second-order problems (2007)
  11. Brugnano, Luigi; Magherini, Cecilia: Economical error estimates for block implicit methods for ODEs via deferred correction. (2006)
  12. Brugnano, Luigi; Magherini, Cecilia; Mugnai, Filippo: Blended implicit methods for the numerical solution of DAE problems (2006)
  13. Brugnano, Luigi; Magherini, Cecilia: The BiM code for the numerical solution of ODEs. (2004)