Research Article
Numerical Treatment on Parabolic Singularly Perturbed Differential Difference Equation via Fitted Operator Scheme
Table 2
Maximum absolute point-wise error rate of convergence for Example
2 before and after Richardson extrapolation method applied, where
, , and
.
| M,N | 16,16 | 32,32 | 64,64 | 128,128 | 256,256 | Before | | 8.9343-03 | 4.4707-03 | 2.2286-03 | 1.1098-03 | 5.5384-04 | | 9.3800-03 | 4.7241-03 | 2.3512-03 | 1.1687-03 | 5.8202-04 | | 9.3844-03 | 4.7269-03 | 2.3526-03 | 1.1693-03 | 5.8233-04 | | 9.3845-03 | 4.7269-03 | 2.3526-03 | 1.1694-03 | 5.8233-04 | | 9.3845-03 | 4.7269-03 | 2.3526-03 | 1.1694-03 | 5.8233-04 | | | | | | | | 9.3845-03 | 4.7269-03 | 2.3526-03 | 1.1694-03 | 5.8233-04 |
| Rate of convergence | | 0.9894 | 1.0066 | 1.0085 | 1.0058 | | After | | 1.8103-03 | 5.1433-04 | 1.5297-04 | 3.9939-05 | 1.0095-05 | | 2.0571-03 | 6.2361-04 | 1.9584-04 | 5.1831-05 | 1.3148-05 | | 2.0599-03 | 6.2482-04 | 1.9636-04 | 5.1977-05 | 1.3185-05 | | 2.0599-03 | 6.2483-04 | 1.9637-04 | 5.1979-05 | 1.3186-05 | | 2.0599-03 | 6.2483-04 | 1.9637-04 | 5.1979-05 | 1.3186-05 | | | | | | | | 2.0599-03 | 6.2483-04 | 1.9637-04 | 5.1979-05 | 1.3186-05 |
| Rate of convergence | | 1.7210 | 1.6699 | 1.9176 | 1.9789 | |
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