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Table 1 Comparison of maximum absolute errors for Example 1

From: Fourth-order fitted mesh scheme for semilinear singularly perturbed reaction–diffusion problems

\(\varepsilon \downarrow N \to\)

32

64

128

256

512

Our method

 \(2^{ - 5}\)

1.2025e−06

7.5262e−08

4.7055e−09

2.9409e−10

1.8195e−11

 \(2^{ - 6}\)

4.2806e−06

2.6824e−07

1.6776e−08

1.0487e−09

6.5420e−11

 \(2^{ - 7}\)

6.7000e−06

4.2429e−07

2.6515e−08

1.6583e−09

1.0359e−10

 \(2^{ - 8}\)

3.7483e−05

2.4697e−06

1.5760e−07

9.9397e−09

6.2393e−10

 \(2^{ - 9}\)

1.4848e−04

1.0348e−05

6.7338e−07

4.2784e−08

2.6937e−09

Results in [14]

 \(2^{ - 5}\)

2.3e−4

5.9e−5

1.5e−5

3.7e−6

9.2e−7

 \(2^{ - 6}\)

3.8e−4

9.5e−4

2.4e−5

6.2e−6

1.5e−6

 \(2^{ - 7}\)

6.4e−4

1.6e−4

4.0e−5

1.0e−5

2.5e−6

 \(2^{ - 8}\)

1.1e−3

2.4e−4

6.9e−5

1.7e−5

4.3e−6

 \(2^{ - 9}\)

1.9e−3

4.9e−4

1.2e−4

3.1e−5

7.6e−6