### A Dimensional Splitting Method for Nonlinear Equations with Variable Coefficients

Knut-Andreas Lie

Abstract: A numerical method is presented for the variable coefficient, nonlinear advection equation $u_t + \sum_{i=1}^d V_i(x,t) f_i(u)_{x_i} = 0$ in arbitrary space dimension for bounded velocities that are Lipschitz continuous in the $x$ variable. The method is based on dimensional splitting and uses a recent front tracking method to solve the resulting one-dimensional non-conservative equations. The method is unconditionally stable, and it produces a subsequence that converges to the entropy solution as the discretization of time and space tends to zero. Three numerical examples are presented.

Paper:
Available as PostScript
Title:
A dimensional splitting method for nonlinear equations with variable coefficients
Author(s):
Knut-Andreas Lie, <andreas@math.ntnu.no>
Publishing information:
Preprint. Mathematics No 17/1997. NTNU.