Theory and Modern Applications
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 |