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Theory and Modern Applications

Table 1 Error estimates and convergence rates for various N for Example  5.1

From: A high-order finite difference scheme for a singularly perturbed reaction-diffusion problem with an interior layer

Number of mesh points N

ε

64

128

256

512

1,024

2,048

10−2

3.4894e−3

1.7662e−4

8.7528e−6

5.5665e−7

3.4830e−8

2.1775e−9

5.535

5.369

4.789

4.715

4.637

-

10−3

7.3009e−3

9.4205e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.799

4.365

3.899

3.977

3.994

-

10−4

7.2974e−3

9.4202e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

10−5

7.2970e−3

9.4220e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

10−6

7.2970e−3

9.4202e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

10−7

7.2970e−3

9.4202e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

10−8

7.2970e−3

9.4202e−4

8.1893e−5

8.6906e−6

8.3929e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

10−9

7.2970e−3

9.4202e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

3.798

4.365

3.899

3.977

3.994

-

\(E^{N}\)

7.3009e−3

9.4205e−4

8.1893e−5

8.6906e−6

8.3930e−7

7.7064e−8

\(R^{N}\)

3.798

4.365

3.899

3.977

3.994

-