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Table 4 Absolute errors for Example 2 given by \(\Vert y_e-y_a\Vert\) are

From: An efficient algorithm to solve damped forced oscillator problems by Bernoulli operational matrix of integration

t

\(m=2\)

\(m=3\)

\(m=5\)

\(m=7\)

\(m=9\)

0.0

7.3937153 \(\times 10^{-3}\)

4.0027165 \(\times 10^{-3}\)

1.187872 \(\times 10^{-4}\)

2.2238 \(\times 10^{-6}\)

8.86\(\times 10^{-8}\)

0.1

1.7293718 \(\times 10^{-3}\)

1.2098059 \(\times 10^{-3}\)

3.90021\(\times 10^{-5}\)

2.310 \(\times 10^{-7}\)

2.72 \(\times 10^{-8}\)

0.2

3.4868805 \(\times 10^{-3}\)

1.5926434 \(\times 10^{-3}\)

3.66331 \(\times 10^{-5}\)

6.928 \(\times 10^{-7}\)

226\(\times 10^{-8}\)

0.3

1.5204341 \(\times 10^{-3}\)

3.54438\(\times 10^{-5}\)

2.05551 \(\times 10^{-5}\)

6.058 \(\times 10^{-7}\)

1.01 \(\times 10^{-8}\)

0.4

1.3499413 \(\times 10^{-3}\)

1.3937426 \(\times 10^{-3}\)

3.19347 \(\times 10^{-5}\)

3.540\(\times 10^{-7}\)

1.07\(\times 10^{-8}\)

0.5

3.3121303\(\times 10^{-3}\)

1.6347759 \(\times 10^{-3}\)

3.2789/2 \(\times 10^{-5}\)

7.238 \(\times 10^{-7}\)

2.25 \(\times 10^{-8}\)

0.6

3.5234170 \(\times 10^{-3}\)

5.969158 \(\times 10^{-4}\)

1.59145\(\times 10^{-5}\)

1.584 \(\times 10^{-7}\)

1.29 \(\times 10^{-8}\)

0.7

1.9275130 \(\times 10^{-3}\)

10241504 \(\times 10^{-5}\)

4.35670 \(\times 10^{-5}\)

7.774 \(\times 10^{-7}\)

7.7\(\times 10^{-9}\)

0.8

9.955869 \(\times 10^{-4}\)

1.9964523\(\times 10^{-3}\)

2.101 \(\times 10^{-7}\)

3.394 \(\times 10^{-7}\)

2.16 \(\times 10^{-8}\)

0.9

4.4842222 \(\times 10^{-3}\)

8.063536 \(\times 10^{-4}\)

5.23268 \(\times 10^{-5}\)

1.870\(\times 10^{-7}\)

2.68 \(\times 10^{-8}\)

1.0

7.7114050\(\times 10^{-3}\)

4.1251090 \(\times 10^{-3}\)

1.187330 \(\times 10^{-5}\)

2.2240 \(\times 10^{-6}\)

8.86 \(\times 10^{-8}\)