| Abstract: | In this article we develop a high‐order Godunov method for one‐dimensional convection‐diffusion‐reaction problems where convection dominates diffusion. The heart of this method comes from incorporating the diffusion term via the slope of the linear representation (recovery) of the solution on each grid cell. The method is conservative and explicit. Therefore, it is efficient in computing time. For constant coefficient linear convection, diffusion, and Lipschitz‐type reaction, the properties of the total variation stability and monotonicity preservation are proved. An error estimation is derived. Computational examples are presented and compared with the exact solutions. © 2000 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 16: 495–512, 2000 |
