English

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

R2 v1 2026-07-22T16:31:19.469Z