Research Article
Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme
Table 1
Maximum absolute point-wise error and rate of convergence for Example
1 before and after Richardson extrapolation method applied, where
, , and
.
| M,N | 32,32 | 64,64 | 128,128 | 256,256 | 512,512 | Before | | 5.5909-03 | 2.7792-03 | 1.3847-03 | 6.9081-04 | 3.4501-04 | | 6.2590-03 | 3.3063-03 | 1.5449-03 | 7.7016-04 | 3.8448-04 | | 6.2656-03 | 3.1096-03 | 1.5465-03 | 7.7096-04 | 3.8488-04 | | 6.2657-03 | 3.1096-03 | 1.5465-03 | 7.7097-04 | 3.8488-04 | | 6.2657-03 | 3.1096-03 | 1.5465-03 | 7.7097-04 | 3.8488-04 | | | | | | | | 6.2657-03 | 3.1096-03 | 1.5465-03 | 7.7097-04 | 3.8488-04 |
| Rate of convergence | | 1.0107 | 1.0077 | 1.0043 | 1.0022 | | After | | 1.8542-04 | 5.5542-05 | 1.5119-05 | 3.9402-06 | 1.0055-06 | | 2.2699-04 | 6.6325-05 | 1.7858-05 | 4.6297-06 | 1.1786-06 | | 2.2742-04 | 6.6437e-05 | 1.7886-05 | 4.6369-06 | 1.1804-06 | | 2.2743-04 | 6.6438-05 | 1.7887-05 | 4.6370-06 | 1.1804-06 | | 2.2743-04 | 6.6438-05 | 1.7887-05 | 4.6370-06 | 1.1804-06 | | | | | | | | 2.2743-04 | 6.6438-05 | 1.7887-05 | 4.6370-06 | 1.1804-06 |
| Rate of convergence | | 1.7753 | 1.8931 | 1.9476 | 1.9739 | |
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