Research Article
Local Discontinuous Galerkin Methods Coupled with Implicit Integration Factor Methods for Solving Reaction-Cross-Diffusion Systems
Table 1
Numerical results for Example
2 at
.
| | | | Order | | Order | | Order | | Order |
| | 42 | 30 | 2.9159E − 1 | — | 1.0756E − 1 | — | 3.9750E − 1 | — | 1.1964E − 1 | — | | 150 | 92 | 1.0714E − 1 | 1.5449 | 3.7922E − 2 | 1.6085 | 1.1495E − 1 | 1.9144 | 4.6267E − 2 | 1.4659 | | 596 | 331 | 2.5577E − 2 | 2.0136 | 1.1788E − 2 | 1.6425 | 2.8564E − 2 | 1.9572 | 1.3543E − 2 | 1.7271 | | 2392 | 1261 | 6.1548E − 3 | 2.2018 | 3.2021E − 3 | 2.0145 | 6.7407E − 3 | 2.2320 | 3.6577E − 3 | 2.0233 | | 9224 | 4739 | 1.5429E − 3 | 2.0212 | 8.5707E − 4 | 1.9255 | 1.6793E − 3 | 2.0304 | 9.7541E − 4 | 1.9309 | | 36838 | 18672 | 3.7359E − 4 | 1.9233 | 2.2556E − 4 | 1.8104 | 4.0320E − 4 | 1.9348 | 2.5540E − 4 | 1.8173 |
| | CPU (s) | | Order | | Order | | Order | | Order |
| | 1.8596 | 0.22 | 5.5622E − 1 | — | 1.6628E − 1 | — | 3.9209E − 1 | — | 1.2379E − 1 | — | | 0.9727 | 0.28 | 1.8244E − 1 | 1.7200 | 5.4618E − 2 | 1.7178 | 1.9275E − 1 | 1.0957 | 7.6123E − 2 | 0.7502 | | 0.4775 | 1.34 | 7.1312E − 2 | 1.3205 | 2.6911E − 2 | 0.9950 | 7.8795E − 2 | 1.2575 | 3.2105E − 2 | 1.2136 | | 0.2501 | 9.75 | 3.1589E − 2 | 1.2586 | 1.3518E − 2 | 1.0643 | 3.5300E − 2 | 1.2412 | 1.5165E − 2 | 1.1593 | | 0.1261 | 86.75 | 1.5204E − 2 | 1.0683 | 6.9372E − 3 | 0.9746 | 1.7065E − 2 | 1.0618 | 7.5730E − 3 | 1.0145 | | 0.0603 | 473.50 | 7.4107E − 3 | 0.9746 | 3.3396E − 3 | 0.9914 | 8.2970E − 3 | 0.9780 | 3.8574E − 3 | 0.9148 |
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