M. Nele et al., Computation of molecular weight distributions by polynomial approximation with complete adaptation procedures, MACROMOL TH, 8(3), 1999, pp. 199-213
The choice of appropriate reference functions is still the major drawback f
or collocation techniques to be used during the computation of molecular we
ight distributions (MWDs) in polymerization reactions and other problems co
nstituted by systems of differential-difference equations. Complete adaptat
ion procedures provide significant improvement of numerical approximations
obtained, but convergence to the real solution is not assured and oscillato
ry numerical approximations may be obtained when the actual solution experi
ences large variations during time integration. An alternative method to co
mpute the reference function in an adaptative manner, called here the integ
ration of the reference function procedure, is presented. The technique is
used to allow the computation of MWDs in two polymerization problems: the m
etallocene-based propene polymerization and the methyl methacrylate/butyl a
crylate emulsion polymerization. The integration of the reference function
procedure allowed the proper computation of broad, bimodal and fast changin
g distributions with polynomials of very low order (below 4), where other a
pproximation techniques failed. The method may be easily implemented and do
es not require any pre-processing before implementation.