| Abstract: |
| A new non-monotone finite difference (FD) method for approximating viscosity solutions of stationary Hamilton-Jacobi problems with Dirichlet boundary conditions will be discussed. The new FD method has local truncation errors that are above the first order Godunov barrier for monotone methods. The method uses a stabilization term called a numerical moment to ensure that the proposed scheme is admissible, stable, and convergent. Numerical tests will be provided that compare the accuracy of the proposed scheme to that of the Lax-Friedrich`s method. |
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