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Theory and Modern Applications

Table 11 Comparison of absolute errors for Example 6 ( \(\pmb{k=3}\) )

From: Numerical solutions for the linear and nonlinear singular boundary value problems using Laguerre wavelets

x

Exact solution

Absolute error M  = 3

Absolute error M  = 4

Absolute error M  = 5

Absolute error M  = 6

Absolute error M  = 7

0.1

0.313265850498063

1.12155e−7

7.47073e−8

7.77016e−11

2.25000e−11

1.12567e−11

0.2

0.3030154228323

1.18254e−7

7.42881e−8

7.21018e−11

2.28459e−11

1.06202e−11

0.3

0.286047265304854

8.26092e−8

6.72829e−8

1.32635e−10

1.64894e−11

9.71828e−12

0.4

0.262531127456033

7.92919e−8

5.59685e−8

1.80870e−10

5.77443e−12

8.57608e−12

0.5

0.232696783873834

3.19442e−8

4.68132e−8

2.27523e−10

2.24772e−12

7.28159e−12

0.6

0.196826805692954

1.34284e−8

3.36344e−8

2.33153e−10

8.22350e−12

5.78329e−12

0.7

0.155248106682756

6.97215e−9

2.21505e−8

2.24769e−10

1.30745e−11

4.31280e−12

0.8

0.108322763444465

3.25668e−8

1.34976e−8

1.93600e−10

1.16738e−11

2.82023e−12

0.9

0.0564386024692362

8.78766e−9

6.50385e−9

8.87945e−11

5.50390e−12

1.33990e−12