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Table 14 Comparison of ECBM results with the exact solution for Example 3 when \(\lambda _{1}=0.000000\), \(\lambda _{2}=0.000000\), and \(n=5\)

From: Extended cubic B-spline method for solving a linear system of second-order boundary value problems

x

Exact solution u(x)

Approx. solution U(x)

Absolute error \(|U(x)-u(x)|\)

Exact solution v(x)

Approx. solution V(x)

Absolute error \(|V(x)-v(x)|\)

0.2

−0.160000

−0.160000

4.163336E−16

0.160000

0.160000

4.718448E−16

0.4

−0.240000

−0.240000

2.775558E−17

0.240000

0.240000

6.106227E−16

0.6

−0.240000

−0.240000

9.992007E−16

0.240000

0.240000

2.775558E−16

0.8

−0.160000

−0.160000

3.469447E−15

0.160000

0.160000

3.691492E−15