Re. Mickens, A FINITE-DIFFERENCE SCHEME FOR TRAVELING-WAVE SOLUTIONS TO BURGERS-EQUATION, Numerical methods for partial differential equations (Print), 14(6), 1998, pp. 815-820
We construct a finite difference scheme for the ordinary differential
equation describing the traveling wave solutions to the Burgers equati
on. This difference equation has the property that its solution can be
calculated. Our procedure for determining this solution follows close
ly the analysis used to obtain the traveling wave solutions to the ori
ginal ordinary differential equation. The finite difference scheme fol
lows directly from application of the nonstandard rules proposed by Mi
ckens. (C) 1998 John Wiley & Sons, Inc.