Numerical analysis of coupled systems of nonlinear parabolic equations

SIAM Journal on Numerical Analysis

Volumn 36, Issue 2, 1999, Pages 393-416

  Pao, C V ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Convergence and error analysis; Finite difference equations; Monotone iterative methods; Reaction diffusion convection; System of parabolic equations

Indexed keywords

EID: 0001326901     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036142996313166     Document Type: Article

References (21)

1. W. F. AMES, Numerical Methods for Partial Differential Equations, 3rd ed., Academic Press, San Diego, 1992.
2. R. ARIS, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Oxford University Press (Clarendon), London, 1975.
3. D. G. ARONSON, The asymptotic speed of propagation of a simple epidemic, in Nonlinear Diffusion (NSF-CBMS Regional Conf. Nonlinear Diffusion Equations, Univ. Houston, Houston, TX, 1976), Res. Notes Math. 14, Pitman, London, 1977, pp. 1-23.
4. W. FENG AND X. LU, Some coexistence and extinction results for a 3-species ecological system, Differential Integral Equations, 8 (1995), pp. 617-629.
5. D. A. FRANK-KAMENETSKII, Diffusion and Heat Transfer in Chemical Kinetics, Plenum Press, New York, 1969.
6. D. GREENSPAN AND S. V. PARTER, Mildly nonlinear partial differential equations and their numerical solution, II, Numer. Math., 7 (1965), pp. 129-146.
7. A. LEUNG, Monotone schemes for semilinear elliptic systems related to ecology, Math. Appl. Sci., 4 (1982), pp. 272-285.
8. C. A. HALL AND T. A. PURSCHING, Numerical Analysis of Partial Differential Equations, Prentice-Hall, Englewood Cliffs, NJ, 1990.
9. D. HOFF, Stability and convergence of finite difference methods for systems of nonlinear reaction-diffusion equations, SIAM J. Numer. Anal., 15 (1978), pp. 1161-1177.
10. A. S. HOUSEHOLDER, The Theory of Matrices in Numerical Analysis, Blaisdell Publishing Co., Ginn and Co., New York, 1964.
11. M. KIRKILIONIS, Mathematical Theory of Horizontal Planktonic Distributions:, Thesis, Ruprecht-Karls-Universität, Heidelberg, 1995.
12. X. LU AND W. FENG, Dynamics and numerical simulation of food-chain populations, Appl. Math. Comput., 65 (1994), pp. 335-344.
13. C. V. PAO, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, 1992.
14. C. V. PAO, Numerical methods for semilinear parabolic equations, SIAM J. Numer. Anal., 24 (1987), pp. 24-35.
15. C. V. PAO, Numerical methods for coupled systems of nonlinear parabolic boundary-value problems, J. Math. Anal. Appl., 151 (1990), pp. 581-608.
16. C. V. PAO, Positive solutions and dynamics of a finite difference reaction-diffusion system, Numer. Methods Partial Differential Equations. 9 (1993), pp. 285-311.
17. C. V. PAO, Blowing-up and asymptotic behaviour of solutions for a finite difference system, Appl. Anal., 62 (1996), pp. 29-38.
18. S. V. PARTER, Mildly nonlinear elliptic partial differential equations and their numerical solution, I, Numer. Math., 7 (1965), pp. 113-128.
19. J. SCHRODER, Operator Inequalities, Academic Press, New York, 1980.
20. W. WALTER, Die linienmethode bei nightlinearen parabolischen differentialglaeichungen, Numer. Math., 12 (1968), pp. 307-321.
21. R. S. VARGA, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1962.