Research Article
Uniformly Convergent Numerical Scheme for Singularly Perturbed Parabolic PDEs with Shift Parameters
Table 1
Example
1, maximum absolute error and rate of convergence for
and
.
| | N = | | | | | | | M = 60 | 120 | 240 | 480 | 960 | 1920 |
| | 5.7729e − 03 | 2.9297e − 03 | 1.4758e − 03 | 7.4067e − 04 | 3.7103e − 04 | 1.8557e − 04 | | 0.9785 | 0.9893 | 0.9946 | 0.9973 | 0.9996 | — |
| | 5.7496e − 03 | 2.9179e − 03 | 1.4699e − 03 | 7.3769e − 04 | 3.6953e − 04 | 1.8494e − 04 | | 0.9785 | 0.9892 | 0.9946 | 0.9973 | 0.9986 | — |
| | 5.7439e − 03 | 2.9150e − 03 | 1.4684e − 03 | 7.3694e − 04 | 3.6916e − 04 | 1.8475e − 04 | | 0.9785 | 0.9893 | 0.9946 | 0.9973 | 0.9987 | — |
| | 5.7424e − 03 | 2.9142e − 03 | 1.4680e − 03 | 7.3676e − 04 | 3.6906e − 04 | 1.8470e − 04 | | 0.9786 | 0.9892 | 0.9946 | 0.9973 | 0.9987 | — |
| | 5.7421e − 03 | 2.9141e − 03 | 1.4679e − 03 | 7.3671e − 04 | 3.6904e − 04 | 1.8469e − 04 | | 0.9785 | 0.9893 | 0.9946 | 0.9973 | 0.9987 | − |
| | 5.7420e − 03 | 2.9140e − 03 | 1.4679e − 03 | 7.3670e − 04 | 3.6904e − 04 | 1.8469e − 04 | | 0.9786 | 0.9892 | 0.9946 | 0.9973 | 0.9987 | — |
| | 5.7420e − 03 | 2.9140e − 03 | 1.4679e − 03 | 7.3670e − 04 | 3.6903e − 04 | 1.8469e − 04 | | 0.9786 | 0.9892 | 0.9946 | 0.9973 | 0.9986 | — |
| | 5.7420e − 03 | 2.9140e − 03 | 1.4679e − 03 | 7.3670e − 04 | 3.6903e − 04 | 1.8468e − 04 | | 0.9786 | 0.9892 | 0.9946 | 0.9973 | 0.9986 | — |
| | 5.7729e − 03 | 2.9297e − 03 | 1.4758e − 03 | 7.4067e − 04 | 3.7103e − 04 | 1.8557e − 04 | | 0.9785 | 0.9892 | 0.9946 | 0.9973 | 0.9987 | — |
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