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Theory and Modern Applications

Table 4 Numerical results for \(\pmb{p=1}\)

From: Multilevel anti-derivative wavelets with augmentation for nonlinear boundary value problems

n

\(\dim S_{n}\)

\(\Vert u-u_{n} \Vert \)

\(\text{Time}_{n}\)

\(\Vert u-u_{1,n-1} \Vert \)

\(\text{Time}_{1,n-1}\)

\(\Vert u-u_{2,n-2} \Vert \)

\(\text{Time}_{2,n-2}\)

\(\Vert u-u_{3,n-3} \Vert \)

\(\text{Time}_{3,n-3}\)

1

3

3.6441e+0

5.5200e–2

4.0184e+0

1.5600e–2

    

2

7

1.6750e+0

3.4570e–1

2.0257e+0

4.5810e–1

1.7817e+0

3.6700e–2

  

3

15

7.4431e–1

2.7760e+0

9.7397e–1

7.0520e–1

8.1878e–1

4.3340e–1

7.6238e–1

1.5370e–1

4

31

3.6599e–1

2.1067e+1

4.8121e–1

7.5820e–1

3.9986e–1

6.5820e–1

3.7317e–1

6.2760e–1

5

63

1.9502e–1

1.6468e+2

2.4916e–1

9.5190e–1

2.0838e–1

8.5460e–1

1.9563e–1

1.1097e+0