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Table 13 Computational time and norms for different optimization equations \(d_{1}(\lambda _{1},\lambda _{2})\), \(d_{2}(\lambda _{1},\lambda _{2})\), and \(d_{3}(\lambda _{1},\lambda _{2})\) with \(n=5\)

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

Minimization values

\(d_{1}(\lambda _{1},\lambda _{2})\)

\(d_{2}(\lambda _{1},\lambda _{2})\)

\(d_{3}(\lambda _{1},\lambda _{2})\)

\(\lambda _{1}\)

0.000000

0.000000

0.000000

\(\lambda _{2}\)

0.000000

0.000000

0.000000

Computational time (s)

7.314018E+01

6.738385E+01

4.973284E+00

\(L_{\infty }\)

3.691492E−15

3.691492E−15

3.691492E−15

\(L_{2}\)

6.058413E−15

6.058413E−15

6.058413E−15