Preprint 1997-030

Front Tracking for One-Dimensional Nonlinear Advection Equations with Variable Coefficients

Knut-Andreas 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 well-defined 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.

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Front tracking for one-dimensional nonlinear advection equations with variable coefficients
Knut-Andreas Lie, <>
Publishing information:
Preprint. Mathematics No 16/1997. NTNU.
Submitted by:
<> November 18 1997.

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