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Table 2 Comparison of maximum absolute errors for Example 1 at number of mesh points 2N

From: Accelerated fitted operator finite difference method for singularly perturbed delay differential equations with non-local boundary condition

ε ↓ N

32

64

128

256

512

Present method

 2−10

6.8161e−06

1.7253e−06

6.3777e−06

5.5050e−05

6.1658e−05

 2−11

6.8161e−06

1.7125e−06

4.3561e−07

1.1065e−07

1.6001e−06

 2−12

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−13

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−14

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−15

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−16

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−17

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−18

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−19

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

 2−20

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

EN

6.8161e−06

1.7125e−06

4.2918e−07

1.0743e−07

2.6874e−08

RN

1.9821

1.9964

1.9982

1.9991

 

Result in [16]

 2−10

5.0010e−03

2.3755e−03

1.1275e−03

5.3851e−04

2.6147e−04

 2−11

5.3378e−03

2.5881e−03

1.2538e−03

6.0996e−04

2.9986e−04

 2−12

5.5738e−03

2.7367e−03

1.3418e−03

6.5956e−04

3.2641e−04

 2−13

5.7397e−03

2.8409e−03

1.4034e−03

6.9419e−04

3.4487e−04

 2−14

5.8565e−03

2.9141e−03

1.4466e−03

7.1844e−04

3.5778e−04

 2−15

5.9389e−03

2.9657e−03

1.4770e−03

7.3548e−04

3.6683e−04

 2−16

5.9970e−03

3.0021e−03

1.4985e−03

7.4747e−04

3.7319e−04

 2−17

6.0380e−03

3.0278e−03

1.5136e−03

7.5592e−04

3.7767e−04

 2−18

6.0670e−03

3.0459e−03

1.5242e−03

7.6189e−04

3.8083e−04

 2−19

6.0875e−03

3.0587e−03

1.5318e−03

7.6610e−04

3.8306e−04

 2−20

6.1020e−03

3.0678e−03

1.5371e−03

7.6907e−04

3.8464e−04

EN

6.1020e−03

3.0678e−03

1.5371e−03

7.6907e−04

3.8464e−04

RN

0.99207

0.99697

0.99904

0.99960