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Advances in Continuous and Discrete Models

Theory and Modern Applications

Table 3 Absolute residuals of numerical solutions for \(h=0.01\)

From: Numerical treatment of nonlinear model of virus propagation in computer networks: an innovative evolutionary Padé approximation scheme

Method

t

VE

VFE

\(\vert \varepsilon_{1} \vert \)

\(\vert \varepsilon _{2} \vert \)

\(\vert \varepsilon_{3} \vert \)

\(\vert \varepsilon_{1} \vert \)

\(\vert \varepsilon_{2} \vert \)

\(\vert \varepsilon_{3} \vert \)

RK-4

0.01

3.7E02

3.7E02

5.5E03

2.4E−02

1.5E−01

2.0E03

0.40

1.5E−04

1.4E−01

6.0E03

2.1E−02

1.0E−01

1.3E03

0.80

3.3E−04

9.5E−02

5.4E03

1.9E−02

6.9E−02

8.8E03

1.20

4.3E−04

6.3E−02

5.0E03

1.7E−02

4.7E−02

5.9E02

1.60

4.6E−04

4.2E−02

4.8E03

1.6E−02

3.3E−02

4.1E02

1.99

4.3E−04

2.8E−04

4.7E03

1.6E−02

2.4E−02

2.9E02

Euler

0.01

2.3E−13

6.8E−13

6.0E03

3.2E−13

2.2E−13

2.0E03

0.40

1.7E−15

1.4E−13

6.0E03

2.4E−13

1.1E−13

1.3E03

0.80

3.6E−15

4.3E−13

5.4E03

2.9E−13

3.2E−14

8.8E02

1.20

3.9E−15

3.3E−14

5.0E03

7.8E−14

3.6E−14

5.9E02

1.60

1.9E−15

3.0E−13

4.8E03

4.5E−13

5.7E−14

4.0E02

1.99

5.6E−16

5.0E−14

4.7E03

1.7E−13

7.9E−14

2.8E02

NSFD

0.01

7.3E02

7.3E02

4.8E03

1.1E−01

3.5E−01

1.9E03

0.40

2.0E−01

4.8E−01

6.0E03

9.0E−02

2.5E−01

1.3E03

0.80

1.6E−01

3.5E−01

5.4E03

7.7E−02

1.8E−01

8.9E02

1.20

1.2E−01

2.5E−01

5.5E03

6.5E−02

1.3E−01

6.0E02

1.60

9.6E−02

1.8E−01

4.8E03

5.6E−02

9.1E−02

4.1E02

1.99

7.3E−02

1.3E−01

4.7E03

4.8E−02

6.7E−02

2.9E02

EPA

0.01

2.2E − 08

9.5E − 08

1.3E − 08

1.9E − 09

1.2E − 11

2.1E − 10

0.40

1.5E − 12

1.2E − 12

6.6E − 14

9.5E − 13

7.1E − 14

9.3E − 14

0.80

2.3E − 13

2.1E − 14

2.8E − 14

6.5E − 13

1.3E − 14

3.5E − 13

1.20

1.8E − 14

5.7E − 14

1.1E − 14

7.8E − 14

2.1E − 15

1.9E − 15

1.60

4.6E − 14

2.8E − 14

4.4E − 15

7.1E − 15

2.2E − 15

6.1E − 17

1.99

5.8E − 14

4.3E − 14

1.7E − 15

1.4E − 14

3.8E − 15

1.1E − 15

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