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Theory and Modern Applications

Table 8 Numerical result of Example 5.7

From: Modified differential transform method for solving linear and nonlinear pantograph type of differential and Volterra integro-differential equations with proportional delays

t

\(u_{E}\)

\(u_{7,R}\)

\(u_{10,R}\)

n = 7, e(u)

n = 10, e(u)

0.1

0.9048374180

0.9048374181

0.9048374181

3.568128916 × 10−11

3.592657686 × 10−11

0.3

0.7408182207

0.7408182191

0.7408182206

1.59385714 × 10−9

1.923883628 × 10−11

0.5

0.6065306597

0.6065305680

0.6065306598

9.1750016 × 10−8

1.80099255 × 10−11

0.7

0.4965853038

0.4965839780

0.4965853044

1.32589299 × 10−6

4.49700608 × 10−10

0.9

0.4065696597

0.4065599623

0.4065696671

9.69737847 × 10−6

7.35104179 × 10−9