Skip to main content Accessibility help
×
Hostname: page-component-76fb5796d-skm99 Total loading time: 0 Render date: 2024-04-25T11:34:42.265Z Has data issue: false hasContentIssue false

6 - Numerical Methods for Chemical Systems

Published online by Cambridge University Press:  15 May 2017

Guy P. Brasseur
Affiliation:
Max-Planck-Institut für Meteorologie, Hamburg
Daniel J. Jacob
Affiliation:
Harvard University, Massachusetts
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2017

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Byrne, G. D. and Hindmarsh, A. C. (1975) A polyalgorithm for the numerical solution of ordinary differential equations, ACM Trans. Math. Softw., 1, 7196.CrossRefGoogle Scholar
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.Google Scholar
Gear, C. W. (1971) Numerical Initial Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
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.Google Scholar
Hairer, E. and Wanner, G. (1996) Solving Ordinary Differential Equations II. Stiff and Differential Algebraic Problems, Springer, New York.Google Scholar
Hairer, E., Norsett, S. P. and Wanner, G. (1993) Solving Ordinary Differential Equations I. Nonstiff Problems, 2nd edition, Springer, New York.Google Scholar
Hairer, E., Lubich, C., and Wanner, G. (2002) Geometric Numerical Integration, Structure Preserving Methods for Ordinary Differential Equations, Springer Verlag, Berlin.Google Scholar
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.Google Scholar
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.Google Scholar
Hindmarsh, A. C. (1977), GEARB: Solution of Ordinary Differential Equations Having Banded Jacobian, LLNL, Report UCID 30059, Rev. 2.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar
Rosenbrock, H. H. (1963) Some general implicit processes for the numerical solution of differential equations, J. Comput., 5, 329330.CrossRefGoogle Scholar
Sandilands, J. and McConnell, J. (1997), Evaluation of a reduced Jacobian chemical solver, J. Geophys. Res., 102 (D15), 1907319087Google Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
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.Google Scholar
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.CrossRefGoogle Scholar
Shimazaki, T. (1985) Minor Constituents in the Middle Atmosphere, D. Reidel, Norwell, MA.Google Scholar
Verwer, J. G. (1994) Explicit methods for stiff ODEs from atmospheric chemistry. In Numerical Mathematics Conference NUMDIFF-7, Halle, Germany.Google Scholar
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.Google Scholar
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.Google Scholar
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.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×