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.
Please, reference the codes as follows:
L.Brugnano, C.Magherini. The BiM Code for the Numerical Solution of ODEs, Jour. Comput. Appl. Mathematics 164–165 (2004) 145–158.
L.Brugnano, C.Magherini, F.Mugnai. Blended Implicit Methods for the Numerical Solution of DAE Problems, Jour. Comput. Appl. Mathematics189 (2006) 34-50.