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Theory and Modern Applications

Table 5 Numerical result of Example 5.4

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

t

\(u_{E}\)

\(u_{7,R}\)

\(u_{11,R}\)

n = 7, e(u)

n = 11, e(u)

0.1

0.2003335

0.2003335

0.2003335

3.964923968 × 10−11

3.965475164 × 10−11

0.3

0.6090405873

0.6090405868

0.6090405869

5.1527572 × 10−10

4.067048190 × 10−10

0.5

1.042190611

1.042190600

1.042190611

1.0808188 × 10−8

1.914523041 × 10−11

0.7

1.517167403

1.517167180

1.517167403

2.2275522 × 10−7

6.429500776 × 10−10

0.9

2.053033451

2.053031300

2.053033451

2.1506409 × 10−6

3.3635213 × 10−10