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Table 6 Numerical results of Example 4 for \(\varepsilon =0.01\)

From: A uniformly valid approximation algorithm for nonlinear ordinary singular perturbation problems with boundary layer solutions

x

UVA solution

SCEM approximation

Absolute error

0.000

−1.0000000000000

−1.0000000000000

0.0000000000000

0.001

−0.5813960926361

−0.5791385346450

2.2575579e(−3)

0.005

1.1529592608432

1.1618243705484

8.8651097e(−3)

0.010

2.4659396723180

2.4727365388982

6.7968665e(−3)

0.050

3.0494963201391

3.0494968235068

5.0336773e(−7)

0.070

3.0694999908694

3.0694999930517

2.1823303e(−9)

0.100

3.0994999999988

3.0994999999993

4.689582e(−13)

0.200

3.1995000000000

3.1995000000000

0.000000000000

0.400

3.3995000000000

3.3995000000000

0.000000000000

0.600

3.5995000000000

3.5995000000000

0.000000000000

0.800

3.7995000000000

3.7995000000000

0.000000000000

1.000

3.9995000000000

3.9995000000000

0.000000000000