Larkin — A Software Package for the Numerical Simulation of LARge Systems Arising in Chemical Reaction KINetics

Chemical reaction kinetics is one of the most important fields of applications where stiff ordinary differential equations occur. In fact, even the term ‘stiff’ originated from chemical kinetics -see CURTISS and HIRSCHFELDER [4.1], who suggested the use of backward differentiation formulae (BDF). These formulae have been selected by GEAR [4.2] in 1971 for his famous implicit multistep code DIFSUB. In order to facilitate the application of this stiff integrator, DIFSUB was later combined with certain chemical kinetics packages such as BELLCHEM due to EDELSON [4.3], HAVCHM due to STABLER and CHESICK [4.4], or KINRATE due to EDSBERG and UHLEN [4.5]. A further important progress was the development of the code called GEAR due to HINDMARSH [4.6]. That code was also (essentially) implemented in the systems FACSIMILE (see CURTIS [4.7]) and MACKSIM due to CARVER and BOYD [4.8].

[1]  P. Rentrop,et al.  Generalized Runge-Kutta methods of order four with stepsize control for stiff ordinary differential equations , 1979 .

[2]  L. A. Farrow,et al.  The steady‐state approximation: Fact or fiction? , 1974 .

[3]  M. B. Carver,et al.  A Program package using stiff, sparse integration methods for the automatic solution of mass action kinetics equations , 1979 .

[4]  J. Douglas Faires,et al.  Numerical Analysis , 1981 .

[5]  Klaus H. Ebert,et al.  The Thermal Decomposition of n-Hexane: Kinetics, Mechanism, and Simulation , 1981 .

[6]  D. Edelson,et al.  A simulation language and compiler to aid computer solution of chemical kinetic problems , 1976, Comput. Chem..

[7]  F. Hoppensteadt,et al.  Numerical Treatment of Rapid Chemical Kinetics by Perturbation and Projection Methods , 1981 .

[8]  B. Hess,et al.  METABOLIC CONTROL MECHANISMS. VII.A DETAILED COMPUTER MODEL OF THE GLYCOLYTIC PATHWAY IN ASCITES CELLS. , 1964, The Journal of biological chemistry.

[9]  C F Curtiss,et al.  Integration of Stiff Equations. , 1952, Proceedings of the National Academy of Sciences of the United States of America.

[10]  S. Benson.  foundations of chemical kinetics , 1960 .

[11]  A. Hindmarsh,et al.  GEAR: ORDINARY DIFFERENTIAL EQUATION SYSTEM SOLVER. , 1971 .

[12]  A. H. Sherman.  NSPIV: a Fortran Subroutine for Gaussian Elimination with Partial Pivoting , 1977 .

[13]  Germund Dahlquist,et al.  Are the numerical methods and software satisfactory for chemical kinetics , 1982 .

[14]  T. E. Hull,et al.  Comparing numerical methods for stiff systems of O.D.E:s , 1975 .

[15]  P. H. Lindsay.  Human Information Processing , 1977 .

[16]  C. W. Gear,et al.  Algorithm 407: DIFSUB for solution of ordinary differential equations [D2] , 1971, Commun. ACM.

[17]  J. P. Chesick,et al.  A program system for computer integration of multistep reaction rate equations using the gear integration method , 1978 .

[18]  R. M. Noyes,et al.  Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction , 1974 .