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Table 8 Numerical results for Example 4

From: Twelfth degree spline with application to quadrature

x

Cubic Subbotin spline (Rathod et al. 2010)

Our spline (degree 12)

Exact

0.08

0.03188137343786

0.03188137201399

0.03188137201399

0.16

0.06355946719297

0.06355946289143

0.06355946289143

0.24

0.09483487811231

0.09483487169780

0.09483487169780

0.32

0.12551584316831

0.12551583472332

0.12551583472332

0.40

0.15542175168553

0.15542174161032

0.15542174161032

0.48

0.18438631483954

0.18438630348378

0.18438630348378

0.56

0.21226029337979

0.21226028115097

0.21226028115097

0.64

0.23891371300311

0.23891370030714

0.23891370030714

0.72

0.26423751498017

0.26423750222075

0.26423750222075

0.80

0.28814461385800

0.28814460141660

0.28814460141660

0.88

0.31057035699849

0.31057034522329

0.31057034522329

0.96

0.33147240333869

0.33147239253316

0.33147239253316

1.04

0.35083005925386

0.35083004966900

0.35083004966902

1.12

0.36864312712815

0.36864311895727

0.36864311895727

1.20

0.38493033640194

0.38493032977830

0.38493032977829

1.28

0.39972743704822

0.39972743204556

0.39972743204556

1.36

0.41308504141739

0.41308503805292

0.41308503805292

1.44

0.42506630222622

0.42506630046567

0.42506630046567

1.52

0.43574451241669

0.43574451218106

0.43574451218106

1.60

0.44520070712697

0.44520070830044

0.44520070830044

1.68

0.45352133969787

0.45352134213630

0.45352134213628

1.76

0.46079609317294

0.46079609671252

0.46079609671252

1.84

0.46711587687507

0.46711588134084

0.46711588134084

1.92

0.47257104508264

0.47257105029616

0.47257105029616

2.00

0.47724986226558

0.47724986805180

0.47724986805182

2.08

0.48123722737203

0.48123723356506

0.48123723356506

2.16

0.48461365876857

0.48461366521607

0.48461366521607

2.24

0.48745453199754

0.48745453856405

0.48745453856405

2.32

0.48982955476235

0.48982956133128

0.48982956133128

2.40

0.49180245760085

0.49180246407540

0.49180246407540

2.48

0.49343087456130

0.49343088086445

0.49343088086445

2.56

0.49476638576280

0.49476639183644

0.49476639183644

2.64

0.49585469283547

0.49585469863896

0.49585469863896

2.72

0.49673589867582

0.49673590418410

0.49673590418411

2.80

0.49744486446812

0.49744486966957

0.49744486966957

2.88

0.49801161925099

0.49801162414511

0.49801162414511

2.96

0.49909574075267

0.49846180478826

0.49846180478826

3.04

0.49931285825549

0.49881710925690

0.49881710925690

3.12

0.49948096097656

0.49909574480018

0.49909574480018

3.20

0.49961028423860

0.49931286206208

0.49931286206208

3.28

0.49970913967489

0.49948096456679

0.49948096456679

3.36

0.49978422351271

0.49961028763743

0.49961028763742

3.44

0.49984088844420

0.49970914290671

0.49970914290671

3.52

0.49988338016042

0.49978422660071

0.49978422660071

3.60

0.49991504054429

0.49984089140984

0.49984089140984

3.68

0.49993848013798

0.49988338302318

0.49988338302318

3.76

0.49993848013798

0.49991504332150

0.49991504332150

3.84

0.49993848013798

0.49993848284482

0.49993848284482

3.92

0.49995572286615

0.49995572551569

0.49995572551569

4.00

0.49996832612598

0.49996832875817

0.49996832875817