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Theory and Modern Applications

Table 2 Example 6.2 corresponding maximum pointwise errors and the rate of convergence such as \(E_{\varepsilon }^{N,\Delta t}\), \(E^{N,\Delta t}\), \(p^{N,\Delta t}\)

From: Finite difference scheme for singularly perturbed reaction diffusion problem of partial delay differential equation with nonlocal boundary condition

ε

N = 8

N = 16

N = 32

N = 64

N = 128

N = 256

N = 512

Δt = 0.1

Δt = 0.1/2

Δt = 0.1/22

Δt = 0.1/23

Δt = 0.1/24

Δt = 0.1/25

Δt = 0.1/26

1

1.9169e−01

1.8765e−01

1.4776e−01

9.7571e−02

5.7092e−02

3.1057e−02

1.6222e-02

10−1

2.0157e−01

1.5386e−01

9.9026e−02

5.6998e−02

3.0701e−02

1.5952e−02

8.1328e-03

10−2

1.9835e−01

1.4615e−01

9.1730e−02

5.1998e−02

2.7761e−02

1.4356e−02

7.3013e-03

10−3

1.9792e−01

1.4531e−01

9.0969e−02

5.1441e−02

2.7447e−02

1.4189e−02

7.2176e-03

10−4

1.9789e−01

1.4523e−01

9.0893e−02

5.1389e−02

2.7427e−02

1.4176e−02

7.2080e-03

10−5

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7429e−02

1.4176e−02

7.2082e-03

10−6

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7430e−02

1.4177e−02

7.2085e-03

10−7

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7430e−02

1.4177e−02

7.2086e-03

10−8

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7431e−02

1.4177e−02

7.2087e-03

10−9

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7431e−02

1.4177e−02

7.2087e-03

10−10

1.9788e−01

1.4522e−01

9.0885e−02

5.1384e−02

2.7431e−02

1.4177e−02

7.2087e-03

\(E^{N,\Delta t}\)

2.0157e−01

1.8765e−01

1.4776e−01

9.7571e−02

5.7092e−02

3.1057e−02

1.6222e-02

\(p^{N,\Delta t}\)

1.0324e−01

3.4479e−01

5.9873e−01

7.7316e−01

8.7837e−01

9.3697e−01