Preprint 1997031
A Dimensional Splitting Method for Nonlinear Equations with Variable
Coefficients
KnutAndreas 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
onedimensional nonconservative 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):
 KnutAndreas 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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