A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
Numerical Analysis
2025-10-20 v1 Numerical Analysis
Analysis of PDEs
Abstract
We present a new third-order, semi-discrete, central method for approximating solutions to multi-dimensional systems of hyperbolic conservation laws, convection-diffusion equations, and related problems. Our method is a high-order extension of the recently proposed second-order, semi-discrete method in [16]. The method is derived independently of the specific piecewise polynomial reconstruction which is based on the previously computed cell-averages. We demonstrate our results, by focusing on the new third-order CWENO reconstruction presented in [21]. The numerical results we present, show the desired accuracy, high resolution and robustness of our method.
Keywords
Cite
@article{arxiv.math/0002133,
title = {A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations},
author = {Alexander Kurganov and Doron Levy},
journal= {arXiv preprint arXiv:math/0002133},
year = {2025}
}
Comments
23 pages, for figures contact Doron Levy or visit his web page