Determining polymer chain length distributions using numerical inversion of Laplace transforms

Polymer Reaction Engineering

Volumn 4, Issue 4, 1996, Pages 279-301

  Miller, N C ^a   Toffolo, R W ^a   McAuley, K B ^a   McLellan, P J ^a  

^a QUEEN S UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; LAPLACE TRANSFORMS; MOLECULAR WEIGHT DISTRIBUTION; PARTIAL DIFFERENTIAL EQUATIONS; POLYMERS; PROBLEM SOLVING;

NUMERICAL INVERSION; POLYMER CHAINS; POLYMER REACTION PROBLEMS; TALBOT'S METHOD; WEEKS' METHOD;

POLYMERIZATION;

EID: 0030284139     PISSN: 10543414     EISSN: None     Source Type: Journal    
DOI: 10.1080/10543414.1996.10744477     Document Type: Article

References (18)

1. Bamford, C. H. and H. Tompa (1954). The calculation of molecular weight distributions from kinetic schemes. Trans. Faraday Soc., 50, 1097-1115.
2. Budde, U. and M. Wulkow (1991). Computation of molecular weight distributions for free radical polymerization systems. Chem. Eng. Sci., 46 (2), 497-508.
3. Davies, B. and B. Martin (1979). Numerical inversion of the Laplace transform: a survey and comparison of methods. J. Comput. Phys, 33, 1.
4. Garbow, B., G. Giunta, J. Lyness and A. Murli (1988). Software for an implementation of Weeks' Method for the inverse Laplace transform problem. ACM Trans. Math. Soft., 14 (2), 163.
5. Giunta, G., G. Laccetti and M. Rizzardi (1988). More on the Weeks method for the numerical inversion of the Laplace transform. Numer. Math., 54, 193.
6. Henrici, P., "Applied and Computational Complex Analysis, v. 1", John Wiley & Sons, Toronto, 1974.
7. Hindmarsh, A. (1980). LSODE and LSODI, two new initial value ordinary differential equation solvers. ACM-Signum Newsletter, 15 (4), 10-11.
8. Lyness, J. and G. Giunta (1986). A modification of the Weeks method for numerical inversion of the Laplace transform. Math. Comput., 47 (175), 313.
9. Mills, P. (1986). Determination of polymer chain length distributions by numerical inversion of z-transforms. Comp. Chem. Eng., 10 (4), 399-420.
10. Murli, A. and M. Rizzardi (1990). Algorithm 682-Talbot's method for the Laplace inversion problem. ACM Trans. Math. Soft., 16 (2), 158.
11. Ray, W. (1972). On the mathematical modeling of polymerization reactors. J. Macromol. Sci.-Rev. Macromol. Chem., C8, 1.
12. Talbot, A. (1979). The accurate numerical inversion of Laplace transforms. J. Inst. Maths. Applics., 23, 97.
13. Tobita, H. (1992). Kinetics of long-chain branching via chain transfer to polymer. ii. new theory to predict molecular weight distribution. Polymer Reaction Eng., 1 (3), 379.
14. Tobita, H. and K. Ito (1992). On the calculation of molecular weight distribution from the moments using laguerre polynomials. Polymer Reaction Eng., 1 (3), 407.
15. Toffolo, R., M. Sc. Thesis, Department of Chemical Engineering, Queen's University, 1995.
16. Weeks, W. (1966). Numerical inversion of Laplace transforms using Laguerre polynomials. J. Assoc. Comp. Mach., 13 (3), 419.
17. Wilkinson, R., 4th Year Thesis, Department of Mathematics and Statistics, Queen's University, 1992.
18. Zeman, R. and N. Amundson (1963). Continuous models for polymerization. AIChE Journal, 9, 297.