Abstract:We introduce two kinds of explicit solutions to the convection-reaction equation,u and employ them to test properties of various computational schemes. From this test we observe that computed solutions using Lax-Friedrichs, MacCormack and Lax-Wendroff schemes break down in a finite time. On the other hand some other schemes including WENO, NT and Godunov show more stable behavior and the tests provide their detailed behaviors. It is discussed that if a numerical scheme is applied to this problem together with the splitting method, certain defects of the scheme can be magnified exponentially and observed easily. Sometimes such a behavior destroys the numerical solution completely and hence one need to pay extra caution to deal with reaction dominant systems._{t}+(|u|^{q}/q)_{x}=u, u,x∈R, t∈R^{+}, q>1,

**Paper:**- Available as PDF (504 Kbytes).
**Author(s):**- Youngsoo Ha, <young@amath.kaist.ac.kr>
- Yong-Jung Kim, <ykim@amath.kaist.ac.kr>
**Publishing information:**- submitted to J. Comput. Phys.
**Comments:****Submitted by:**- <ykim@amath.kaist.ac.kr> September 23 2005.

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