Discretizations of nonlinear differential equations using explicit nonstandard methods

Journal of Computational and Applied Mathematics

Volumn 110, Issue 1, 1999, Pages 181-185

  Mickens, Ronald E ^a  

^a CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

34A50; 65L06; Nonstandard finite difference scheme; Spurious solution

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; FINITE DIFFERENCE METHOD; MATHEMATICAL MODELS; RUNGE KUTTA METHODS;

MONOD EQUATIONS; NONSTANDARD FINITE DIFFERENCE SCHEME; SPURIOUS SOLUTION;

ORDINARY DIFFERENTIAL EQUATIONS;

EID: 0033338885     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(99)00233-2     Document Type: Article

References (7)

1. Chen B., Solis F. Discretizations of nonlinear differential equations using explicit finite order methods. J. Comput. Appl. Math. 90:1998;171-183.
2. F.B. Hildebrand, Finite-Difference Equations and Simulations, Prentice-Hall, Englewood Cliffs, NJ, 1968.
3. R.E. Mickens, Difference Equations - Theory and Applications, Van Nostrand Reinhold, New York, 1990.
4. Mickens R.E. Comments on A second-order chaos-free explicit method problem in neurophysiology. Numer. Methods Partial Differential Equations. 10:1994;587-590.
5. R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
6. Mickens R.E., Ramadhani I. Finite-differences having the correct linear stability properties for all finite step-sizes III. Comput. Math. Appl. 27:1994;77-89.
7. Potts R.B. Differential equations and difference equations. Math. Monthly. 89:1982;402-407.