Skip to main content Accessibility help
×
Home
  • Print publication year: 2017
  • Online publication date: May 2017

6 - Numerical Methods for Chemical Systems

Related content

Powered by UNSILO
Byrne, G. D. and Hindmarsh, A. C. (1975) A polyalgorithm for the numerical solution of ordinary differential equations, ACM Trans. Math. Softw., 1, 7196.
Dabdub, D. and Seinfeld, J. H. (1995) Extrapolation techniques used in the solution of stiff ODEs associated with chemical kinetics of air quality models, Atmos. Environ., 29, 403410.
Gear, C. W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.
Gong, W. and Cho, H.-R. (1993) A numerical scheme for the integration of the gas phase chemical rate equations in a three-dimensional atmospheric models, Atmos. Environ., 27A (14), 21472160.
Hairer, E. and Wanner, G. (1996) Solving Ordinary Differential Equations II. Stiff and Differential Algebraic Problems, Springer, New York.
Hairer, E., Norsett, S. P. and Wanner, G. (1993) Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd edition, Springer, New York.
Hairer, E., Lubich, C., and Wanner, G. (2002) Geometric Numerical Integration, Structure Preserving Methods for Ordinary Differential Equations, Springer Verlag, Berlin.
Hertel, O., Berkowicz, R., and Christensen, J. (1993) Test of two numerical schemes for use in atmospheric transport-chemistry models, Atmos. Environ., 27A, 16, 25912611.
Hesstvedt, E., Hov, O., and Isacksen, I. (1978) Quasi-steady-state-approximation in air pollution modelling: Comparison of two numerical schemes for oxidant prediction, Int. J. Chem. Kinet., 10, 971994.
Hindmarsh, A. C. (1977), GEARB: Solution of Ordinary Differential Equations Having Banded Jacobian, LLNL, Report UCID 30059, Rev. 2.
Jay, L. O., Sandu, A., Potra, F. A., and Carmichael, G. R. (1995) Improved QSSA methods for atmospheric chemistry integration. Reports on Computational Mathematics No 67/1995, Dept. Mathematics, University of Iowa.
Press, W. H., Teukolsky, S. A., Vetterling, W. T., and Flannery, B. P. (2007) Numerical Recipes: The Art of Scientific Computing, 3rd edition, Cambridge University Press, Cambridge.
Ramaroson, R., Pirre, M., and Cariolle, D. (1992) A box model for on-line computations of diurnal variations in multidimensional models: Application to the one-dimensional case, Ann. Geophys., 10, 416428.
Rosenbrock, H. H. (1963) Some general implicit processes for the numerical solution of differential equations, J. Comput., 5, 329330.
Sandilands, J. and McConnell, J. (1997), Evaluation of a reduced Jacobian chemical solver, J. Geophys. Res., 102 (D15), 1907319087
Sandu, A., Verwer, J. G., Blom, J. G., et al. (1997a) Benchmarking stiff ODE solvers for atmospheric chemistry problems II: Rosenbrock solvers, Atmos. Environ., 31 (20), 34593472.
Sandu, A., Verwer, J. G., Van Loon, M., et al. (1997b) Benchmarking stiff ODE solvers for atmospheric chemistry problems I: Implicit vs explicit, Atmos. Environ., 31 (19), 31513166.
Santillana, M., Le Sager, P., Jacob, D. J., and Brenner, M. P. (2010) An adaptive reduction algorithm for efficient chemical calculations in global atmospheric chemistry models, Atmos. Environ., 44, 35, 44264431.
Saylor, R. D. and Ford, G. D. (1995) On the comparison of numerical methods for the integration of kinetic equations in atmospheric chemistry and transport models, Atmos. Environ., 29 (19), 25852593.
Shimazaki, T. (1985) Minor Constituents in the Middle Atmosphere, D. Reidel, Norwell, MA.
Verwer, J. G. (1994) Explicit methods for stiff ODEs from atmospheric chemistry. In Numerical Mathematics Conference NUMDIFF-7, Halle, Germany.
Verwer, J. G., Spee, E. J., Blom, J. G., and Hundsdorfer, W. (1999) A second-order Rosenbrock method applied to photochemical dispersion problems, SIAM J. Sci. Comput., 20 (4), 14561480.
Young, T. R. and Boris, J. P. (1977) A numerical technique for solving stiff ordinary differential equations associated with the chemical kinetics of reactive flow problems, J. Phys. Chem., 81, 24242427.
Zhang, H., Linford, J. C., Sandu, A., and Sander, R. (2011) Chemical mechanism solvers in air quality models, Atmosphere, 2, 510532, doi: 10.3390/atmos2030510.