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Theory and Modern Applications

Table 4 Numerical result of Example 5.3

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

t

\(u_{E}\)

\(u_{8,R}\)

\(u_{11,R}\)

n = 8, e(u)

n = 11, e(u)

0.1

0.09048374180

0.09048374181

0.09048374181

3.568128916 × 10−12

3.592657686 × 10−12

0.3

0.2222454662

0.2222454658

0.2222454663

4.6785714 × 10−10

4.528351013 × 10−12

0.5

0.3032653298

0.3032652840

0.3032653298

4.58254531 × 10−8

5.85598678 × 10−11

0.7

0.3476097127

0.3476087846

0.3476097130

9.2816132 × 10−7

2.78563346 × 10−10

0.9

0.3659126937

0.3659039660

0.3659127002

8.72761061 × 10−6

6.64594981 × 10−9