Table 4 Numerical results of Example 3 for \(\varepsilon =0.01\)
x | Asymptotic solution (O’Malley 1974) | SCEM approximation | Absolute error |
|---|---|---|---|
0.000 | 0.0000000000 | 0.0000000000 | 0.0000000000 |
0.001 | −0.0476179808 | −0.0476179344 | 4.633630e(−8) |
0.005 | −0.1998179193 | −0.1998178062 | 1.130920e(−7) |
0.010 | −0.3317348800 | −0.3317346943 | 1.857260e(−7) |
0.050 | −0.6496961369 | −0.6496952868 | 8.501800e(−7) |
0.100 | −0.6835976643 | −0.6835975658 | 9.854120e(−8) |
0.200 | −0.6683483288 | −0.6683483281 | 6.84303e(−10) |
0.300 | −0.6371090868 | −0.6371090868 | 4.61752e(−12) |
0.400 | −0.5927835996 | −0.5927835996 | 3.10862e(−14) |
0.500 | −0.5347999967 | −0.5347999967 | 2.22044e(−16) |
0.600 | −0.4623401221 | −0.4623401221 | 1.11022e(−16) |
0.700 | −0.3743118452 | −0.3743118452 | 0.0000000000 |
0.800 | −0.2692764695 | −0.2692764695 | 0.0000000000 |
0.900 | −0.1453415344 | −0.1453415344 | 0.0000000000 |
1.000 | 0.0000000000 | 0.0000000000 | 0.0000000000 |