Numerical Stationary Solutions for a Viscous Burgers' Equation

This paper is concerned with an interesting numerical anomaly associated with steady state solutions for the viscous Burgers' equation. In particular, we consider Burgers' equation on the interval (0; 1) with Neumann boundary conditions. In this work we show that even for moderate values of the viscosity and for certain initial conditions, numerical solutions approach nonconstant shock type stationary solutions. This is rather curious since we also show that the only possible actual stationary solutions are constants. In order to provide a reasonable explanation for this numerical anomaly, we show that the solutions obtained correspond to solutions of a related problem considered recently by L.G. Reyna and M.J. Ward [15].