Preprint 1997030
Front Tracking for OneDimensional Nonlinear Advection Equations with
Variable Coefficients
KnutAndreas Lie
Abstract:
A new front tracking method is developed for the variable coefficient
equation $u_t + V(x,t)f(u)_x = 0$. The method is a generalization of
Dafermos' method for the constant coefficient case and is welldefined
also for certain discontinuous velocities $V$. We give an explicit
inequality stating the stability with respect to flux function, velocity,
and initial data. The numerical method is unconditionally stable and has
linear convergence. It is well suited for numerical calculations, as is
demonstrated in three examples.
 Paper:
 Available as PostScript
 Title:
 Front tracking for onedimensional nonlinear advection equations with
variable coefficients
 Author(s):
 KnutAndreas Lie,
<andreas@math.ntnu.no>
 Publishing information:
 Preprint. Mathematics No 16/1997. NTNU.
 Comments:

 Submitted by:

<andreas@math.ntnu.no>
November 18 1997.
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