A Finite Difference Scheme for Traveling Wave Solutions to Burgers Equation

Numerical Methods for Partial Differential Equations

Volumn 14, Issue 6, 1998, Pages 815-820

  Mickens, Ronald E ^a  

^a CLARK ATLANTA UNIVERSITY   (United States)

Author keywords

Burgers equation; Exact solutions; Nonstandard finite difference schemes; Traveling waves

Indexed keywords

EID: 0001005409     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(199811)14:6<815::AID-NUM5>3.0.CO;2-T     Document Type: Article

References (10)

1. G. B. Whitham, Linear and Nonlinear Waves, Wiley, New York, 1974.
2. J. D. Logan, Nonlinear Partial Differential Equations, Wiley, New York, 1994.
3. B. Zinner, "Existence of traveling wavefront solutions for the discrete Nagumo equation," J. Differential Eq. 96, 1 (1992).
4. G. Harris, W. Hudson, and B. Zinner, "Traveling wavefronts for the discrete Fisher's equation," J. Differential Eq. 105, 46 (1993).
5. B. Zinner, "Stability of traveling wavefronts for the discrete Nagumo equation," SIAM J. Math. Anal. 22, 1016 (1991).
6. R. E. Mickens, "Exact solutions to difference equation models of Burgers equation," Numer. Methods Partial Differential Eq. 2, 213 (1986).
7. R. E. Mickens, "Exact solutions to a finite-difference model of a nonlinear reaction-advection equation: Implications for numerical analysis," Numer. Methods Partial Differential Eq. 5, 313 (1989).
8. R. E. Mickens, Nonstandard Finite Difference Models of Differential Equations, World Scientific, Singapore, 1994.
9. R. E. Mickens and A. Smith, "Finite-difference models of ordinary differential equations: Influence of denominator functions," J. Franklin Institute 327, 143 (1990).
10. R. E. Mickens, Difference Equations: Theory and Applications, Chapman and Hall, New York, 1990.