Preprint 1997-031
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.
- Comments:
-
- Submitted by:
-
<andreas@math.ntnu.no>
November 18 1997.
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Last modified: Tue Nov 18 10:00:13 1997