Nonstandard methods for the convective-dispersive transport equation with nonlinear reactions

Numerical Methods for Partial Differential Equations

Volumn 15, Issue 6, 1999, Pages 617-624

  Kojouharov, Hristo V ^a   Chen, Benito M ^a  

^a UNIVERSITY OF WYOMING   (United States)

Author keywords

Convection dispersion equations; Eulerian Lagrangian methods; Nonstandard finite difference schemes

Indexed keywords

EID: 0010751438     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199911)15:6<617::AID-NUM1>3.0.CO;2-M     Document Type: Article

References (10)

1. K. W. Morton, Numerical solution of convection-diffusion problems, Chapman & Hall, London, 1996.
2. B. Liu, M. B. Allen, H. Kojouharov, and B. Chen, "Finite-element solution of reaction-diffusion equations with advection," Computational methods in water resources XI, Vol. 1: Computational methods in subsurface flow and transport problems, A. A. Aldama, J. Aparicio, C. A. Brebbia, W. G. Gray, I. Herrera, G. F. Pinder (Editors), Computational Mechanics, Southampton, Boston, 1996.
3. H. V. Kojouharov and B. M. Chen, Nonstandard methods for the convective transport equation with nonlinear reactions, Numer Methods Partial Differential Eq 14 (1998), 467-485.
4. A. R. Mitchell and D. F. Griffiths, The finite difference method in partial differential equations, Wiley, New York, 1980.
5. F. John, Partial differential equations, Springer-Verlag, New York, 1991.
6. C. N. Dawson, T. F. Russell, and M. F. Wheeler, Some improved error estimates for the modified method of characteristics, SIAM J Numer Anal 26 (1989), 1487-1512.
7. J. Douglas, Jr. and T. F. Russell, Numerical methods for convection-dominated diffusion problems based on combining the method of characteristics with finite element or finite difference procedures, SIAM J Numer Anal 19 (1982), 871-885.
8. R. E. Mickens, Exact solutions to a finite-difference model of nonlinear reaction-advection equation: Implications for numerical analysis, Numer Methods Partial Differential Eq 5 (1989), 313-325.
9. R. E. Mickens, A best finite-difference scheme for the fisher equation, Numer Methods Partial Differential Eq 10 (1994), 581-585.
10. J. D. Murray, Mathematical biology, Springer, Berlin, 1993.