A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction

Mathematics and Computers in Simulation

Volumn 62, Issue 1-2, 2003, Pages 117-124

  Mickens, Ronald E ^a  

^a CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

Burgers equation; Nonstandard finite difference schemes; Numerical integration

Indexed keywords

BOUNDARY CONDITIONS; NONLINEAR EQUATIONS; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING;

WAVE PROBLEMS;

FINITE DIFFERENCE METHOD;

EID: 0037434501     PISSN: 03784754     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0378-4754(02)00180-5     Document Type: Conference Paper

References (10)

1. L. Debnath, Nonlinear Differential Equations for Scientists and Engineers, Birkhauser, Boston, 1997.
2. J.D. Logan, Nonlinear Partial Differential Equations, Wiley/Interscience, New York, 1994.
3. R.J. LeVeque, Numerical Methods for Conservation Laws, Birkhauser, Basel, 1992.
4. L. Lapidus, G.F. Pinder, Numerical Solutions of Partial Differential Equations in Science and Engineering, Wiley/Interscience, New York, 1982.
5. C.B. Laney, Computational Gasdynamics, Cambridge University Press, New York, 1998.
6. R.E. Mickens, The role of positivity in the construction of nonstandard finite difference schemes for PDE's, in: D. Schultz, et al. (Eds.), Proceedings of International Conference on Scientific Computing and Mathematical Modeling, University of Wisconsin-Milwaukee, Milwaukee, WI, 2000, pp. 294-307.
7. J.D. Murray, Mathematical Biology, Springer, Berlin, 1993.
8. Mickens R.E., Numer. Methods Part. Diff. Eq. 15:1999;201.
9. R.E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Publ. Co., Singapore, 1994.
10. Mickens R.E., Smith A., J. Franklin Inst. 327:1990;143.