Preprint 2000-017

Unconditionally Stable Methods for Hamilton-Jacobi Equations

Kenneth Hvistendahl Karlsen and Nils Henrik Risebro

Abstract: We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton-Jacobi equations of the form $u_{t}+H(D_xu)=0$. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws $p_{t}+D_x H(p) =0$, where $p=D_xu$. In particular, our methods depends heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally in the sense that the time step is not limited by the space and they can be viewed as time step'' Godunov type (or front tracking). We present several numerical examples illustrating main features of the proposed methods. also compare our methods several methods from the literature.

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Kenneth Hvistendahl Karlsen, <>
Nils Henrik Risebro , <>
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<> May 3 2000.

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