Table 3 Computed maximum absolute errors and rate of convergence for Example 2
From: Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems
\(\varepsilon \downarrow N \to\) | 16 | 32 | 64 | 128 | 256 |
|---|---|---|---|---|---|
\(2^{ - 7}\) | 1.1522e−04 | 7.3531e−06 | 4.6790e−07 | 2.9236e−08 | 1.8268e−09 |
3.9699 | 3.9741 | 4.0004 | 4.0004 | 3.9998 | |
\(2^{ - 8}\) | 5.6563e−04 | 4.1555e−05 | 2.7502e−06 | 1.7562e−07 | 1.1074e−08 |
3.7668 | 3.9174 | 3.9690 | 3.9872 | 3.9942 | |
\(2^{ - 9}\) | 1.8378e−03 | 1.5766e−04 | 1.1083e−05 | 7.2268e−07 | 4.5926e−08 |
3.5431 | 3.8304 | 3.9388 | 3.9760 | 3.9896 | |
\(2^{ - 10}\) | 4.1400e−03 | 4.5262e−04 | 3.5704e−05 | 2.4223e−06 | 1.5601e−07 |
3.1933 | 3.6641 | 3.8816 | 3.9567 | 3.9825 |