Computation of molecular weight distributions by polynomial approximation with complete adaptation procedures

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.