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Theory and Modern Applications

Table 1 Comparison of the absolute errors for Example 1

From: A new numerical method to solve pantograph delay differential equations with convergence analysis

r

Taylor method with M = 9

Taylor method with M = 12

presented method with M = 9

presented method with M = 12

0.2

0.70 × 10−14

2.22 × 10−16

4.9 × 10−13

2.22 × 10−15

0.4

0.10 × 10−10

2.22 × 10−15

3.36 × 10−12

3.553 × 10−15

0.6

0.29 × 10−9

2.22 × 10−13

2.504 × 10−11

2.22 × 10−16

0.8

0.38 × 10−8

1.33 × 10−12

4.553 × 10−11

4.44 × 10−16

1

0.29 × 10−7

5.01 × 10−10

4.886 × 10−11

2.665 × 10−15