2025/02/06 by Tom Lewis, Lewis, T., Xiaoping Xue +1 · 1 citation
Mathematics · Computer Science · #Numerical methods for differential equations #Matrix Theory and Algorithms #Mathematical Biology Tumor Growth
paper · pdf · doi:10.48550/arxiv.2502.03728
A new class of non-monotone finite difference (FD) approximation methods for approximating solutions to non-degenerate stationary Hamilton-Jacobi problems with Dirichlet boundary conditions is proposed and analyzed. The new FD methods add a high order correction to the Lax-Friedrich's method while utilizing a novel cutoff to preserve the convergence properties of the Lax-Friedrich's approximation. Since monotone methods are limited to first order accuracy by the Godunov barrier, the proposed approach provides a template for boosting the accuracy of a monotone method using a modified numerical moment stabilizer with a high-order auxiliary boundary condition. Numerical tests are provided to test the utility of the approach while a novel admissibility and stability analysis technique lays a foundation for analyzing non-monotone methods.