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Theory and Modern Applications

Table 1 Numerical results for Example 4.1

From: Chebyshev reproducing kernel method: application to two-point boundary value problems

x

Absolute errors: \(\boldsymbol{|u-u_{m}|}\)

m  = 2

m  = 4

m  = 6

m  = 8

m  = 9

0.1

3.7948E − 03

1.9500E − 05

4.2625E − 08

7.7160E − 11

8.3641E − 13

0.2

3.8926E − 03

3.1593E − 06

2.3047E − 09

4.0493E − 11

6.8001E − 13

0.3

1.3057E − 03

8.9693E − 06

1.0733E − 08

5.8828E − 11

7.2092E − 13

0.4

2.9333E − 03

5.7392E − 06

1.8736E − 08

4.3152E − 11

6.5603E − 13

0.5

7.7603E − 03

5.4270E − 06

7.8240E − 09

5.6790E − 11

6.6636E − 13

0.6

1.2072E − 02

9.1774E − 06

7.4446E − 09

8.4509E − 11

5.8942E − 13

0.7

1.4711E − 02

6.7151E − 06

2.4443E − 08

8.5180E − 11

6.4981E − 13

0.8

1.4458E − 02

3.9780E − 05

4.6549E − 09

8.4175E − 11

3.6804E − 13

0.9

1.0016E − 02

6.0631E − 05

1.2269E − 07

2.7533E − 13

2.0268E − 12

\(\|\varepsilon_{m}\|_{{}^{o}L_{w}^{2}}\)

9.6803E − 03

3.1956E − 05

7.0121E − 08

9.1748E − 11

1.9859E − 12