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A splitting method for the augmented Burgers equation
In this paper we consider a splitting method for the augmented Burgers equation and prove that it is of ﬁrst order. We also analyze the large-time behavior of the approximated solution by obtaining the ﬁrst term in the ...
A semi-discrete large-time behavior preserving scheme for the augmented Burgers equation
In this paper we analyze the large-time behavior of the augmented Burgers equation. We first study the well-posedness of the Cauchy problem and obtain $L^1-L^p$ decay rates. The asymptotic behavior of the solution is ...
Large-time asymptotics, vanishing viscosity and numerics for 1-D scalar conservation laws
In this paper we analyze the large time asymptotic behavior of the discrete solutions of numerical approximation schemes for scalar hyperbolic conservation laws. We consider three monotone conservative schemes that are ...