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Table 7 Numerical results for Example 3

From: Twelfth degree spline with application to quadrature

x

Cubic Subbotin spline (Rathod et al. 2010)

Our spline (degree 12)

Exact

−0.96

0.00159996602042

0.001599965867977

0.001599965867977

−0.92

0.00333302534289

0.003333024742788

0.003333024742788

−0.88

0.00521620933478

0.005216208258150

0.005216208258151

−0.84

0.00726952592022

0.007269524203804

0.007269524203804

−0.80

0.00951662318369

0.009516620655397

0.009516620655397

−0.76

0.01198563460978

0.011985631024242

0.011985631024242

−0.72

0.01471026306531

0.014710258097708

0.014710258097708

−0.68

0.01773118316554

0.017731176373487

0.017731176373487

−0.64

0.02109787092452

0.021097861705018

0.021097861705018

−0.60

0.02487101138281

0.024870998909352

0.024870998909352

−0.56

0.02912569297475

0.029125676114165

0.029125676114165

−0.52

0.03395567758607

0.033955654793668

0.033955654793668

−0.48

0.03947914276296

0.039479111969976

0.039479111969976

−0.44

0.04584642810741

0.045846386655399

0.045846386655399

−0.40

0.05325046504333

0.053250409830185

0.053250409830185

−0.36

0.06194066062908

0.061940588908491

0.061940588908491

−0.32

0.07224083917045

0.072240751098736

0.072240751098736

−0.28

0.08457087983609

0.084570785226588

0.084570785226588

−0.24

0.09946860939441

0.099468543269364

0.099468543269364

−0.20

0.11760046918276

0.117600520709514

0.117600520709514

−0.16

0.13973162302703

0.139731964944293

0.139731964944293

−0.12

0.16659542193349

0.166596253334887

0.166596253334886

−0.08

0.19857766701988

0.198578877966528

0.198578877966530

−0.04

0.23520031780477

0.235201041419030

0.235201041419027

0.00

0.27468081092706

0.274680153389003

0.274680153389003

0.04

0.31416062591739

0.314159265358976

0.314159265358979

0.08

0.35078230627314

0.350781428811479

0.350781428811476

0.12

0.38276433473857

0.382764053443120

0.382764053443120

0.16

0.40962833358333

0.409628341833713

0.409628341833714

0.20

0.43175968738734

0.431759786068493

0.431759786068493

0.24

0.44989165576688

0.449891763508642

0.449891763508642

0.28

0.46478942923129

0.464789521551418

0.464789521551418

0.32

0.47711948282318

0.477119555679270

0.477119555679270

0.36

0.48741966211928

0.487419717869515

0.487419717869515

0.40

0.49610985468976

0.496109896947821

0.496109896947821

0.44

0.50351388804248

0.503513920122607

0.503513920122607

0.48

0.50988117027174

0.509881194808030

0.509881194808030

0.52

0.51540463300912

0.515404651984338

0.515404651984339

0.54

0.52023461579352

0.520234630663842

0.520234630663842

0.60

0.52448929604318

0.524489307868654

0.524489307868654

0.64

0.52826243552178

0.528262445072988

0.528262445072988

0.68

0.53162912256560

0.531629130404519

0.531629130404519

0.72

0.53465004214157

0.534650048680298

0.534650048680298

0.76

0.53737467021086

0.537374675753765

0.537374675753765

0.80

0.53984368134898

0.539843686122609

0.539843686122610

0.84

0.54209077839986

0.542090782574202

0.542090782574202

0.88

0.54414409481617

0.544144098519856

0.544144098519856

0.92

0.54602727870406

0.546027282035218

0.546027282035218

0.96

0.54776033787596

0.547760340910029

0.547760340910029

1.00

0.54936030383282

0.549360306778006

0.549360306778006