Monotone methods for a finite difference system of reaction diffusion equation with time delay

Computers and Mathematics with Applications

Volumn 36, Issue 10-12, 1998, Pages 37-47

  Pao, C V ^a  

^a NORTH CAROLINA STATE UNIVERSITY   (United States)

Author keywords

Finite difference equations; Monotone iterations; Reaction diffusion; Time delay; Upper and lower bounds

Indexed keywords

ALGORITHMS; BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; FINITE DIFFERENCE METHOD; ITERATIVE METHODS; NONLINEAR EQUATIONS;

MONOTONE ITERATIONS; NONLINEAR REACTION-DIFFUSION EQUATIONS;

DIFFERENCE EQUATIONS;

EID: 0032203095     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0898-1221(98)80007-2     Document Type: Article

References (15)

1. W.F. Ames, Numerical Methods for Partial Differential Equations, Academic Press, San Diego, CA, (1992).
2. A.R. Mitchell and D.G. Griffiths, The Finite Difference Method in Partial Differential Equations, Wiley, New York, (1980).
3. C.V. Pao, Numerical methods for semilinear parabolic equations, SIAM J. Numer. Anal. 24, 24-35 (1987).
4. C.V. Pao, Positive solutions and dynamics of a finite difference reaction-diffusion system, Numer. Methods Partial Differ. Eqs. 9, 285-311 (1993).
5. G.S. Ladde, V. Lakshmikantham and A.S. Vatsala, Monotone Iterative Techniques for Nonlinear Differential Equations, Pittman, Boston, MA, (1985).
6. C.V. Pao, Nonlinear Parabolic and Elliptic Equations, Plenum Press, New York, (1992).
7. D. Greenspan and S.V. Parter, Mildly nonlinear elliptic partial differential equations and their numerical solution, II, Numer. Math. 7, 129-146 (1965).
8. P.Y.H. Pang and R.P. Agarwal, Monotone iterative methods for a general class of discrete boundary value problems, Computers Math. Applic. 28 (1-3), 243-254 (1994).
9. C.V. Pao, Numerical solutions for some coupled systems of nonlinear boundary value problems, Numer. Math. 51, 381-394 (1987).
10. C.V. Pao, Asymptotic behavior of solutions for finite-difference equations of reaction-diffusion, J. Math. Anal. Appl. 144, 206-225 (1989).
11. R.S. Varga, Matrix Iterative Analysis, Prentice Hall, Englewood Cliffs, NJ, (1962).
12. W. Feng and X. Lu, Asymptotic periodicity in diffusive logistic equations with discrete delay, Nonlinear Analysis, TMA 26, 171-178 (1996).
13. J.D. Murray, Mathematical biology, In Biomathematics, Volume 19, Springer, Berlin, (1989).
14. Y. Yamada, On a certain class of semilinear Volterra diffusion equations, J. Math. Anal. Appl. 88, 433-451 (1982).
15. X. Lu, Persistence and extinction in a competition-diffusion system with time delays, Canadian Appl. Math. Quart. 2, 231-246 (1994).