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Table 3 Numerical results for Example 1

From: Twelfth degree spline with application to quadrature

x Cubic Subbotin spline (Rathod et al. 2010) Natural spline Our spline (degree 12) Exact
1.08 0.03922071396027 0.03922071396027 0.039220713153281 0.039220713153281
1.16 0.07696104319944 0.07695999495151 0.076961041136128 0.076961041136128
1.24 0.11332868821323 0.11332791689560 0.113328685307003 0.113328685307003
1.32 0.14842000880542 0.14841915996469 0.148420005118273 0.148420005118273
1.40 0.18232156111573 0.18232073025801 0.182321556793955 0.182321556793955
1.48 0.21511138448704 0.21511054644682 0.215111379616945 0.215111379616945
1.56 0.24686008326688 0.24685924513945 0.246860077931526 0.246860077931526
1.64 0.27763174233409 0.27763090250854 0.277631736598280 0.277631736598280
1.72 0.30748470582867 0.30748386497839 0.307484699747961 0.307484699747961
1.80 0.33647224300070 0.33647140114729 0.336472236621213 0.336472236621213
1.88 0.36464312022710 0.36464227753464 0.364643113587909 0.364643113587909
1.96 0.39204209464187 0.39204125120987 0.392042087776024 0.392042087776024
2.04 0.41871034192254 0.41870949784609 0.418710334858185 0.418710334858185
2.12 0.44468582850026 0.44468498385764 0.444685821261446 0.444685821261446
2.20 0.47000363663837 0.47000279149742 0.470003629245736 0.470003629245736
2.28 0.49469624936477 0.49469540378362 0.494696241836107 0.494696241836107
2.36 0.51879380106450 0.51879295509338 0.518793793415168 0.518793793415168
2.44 0.54232429858202 0.54232345226443 0.542324290825362 0.542324290825362
2.52 0.56531381690245 0.56531297027618 0.565313809050060 0.565313809050060
2.60 0.58778667284010 0.58778582593813 0.587786664902119 0.587786664902119
2.68 0.60976557963560 0.60976473248676 0.609765571620894 0.609765571620894
2.76 0.63127178492549 0.63127093755506 0.631271776841858 0.631271776841858
2.84 0.65232519418539 0.65232434661562 0.652325186039690 0.652325186039690
2.92 0.67294448144414 0.67294363369464 0.672944473242426 0.672944473242426
3.00 0.69314718881230 0.69314634090043 0.693147180559945 0.693147180559945
3.08 0.71294981615437 0.71294896809550 0.712949807856125 0.712949807856125
3.16 0.73236790205313 0.73236705386091 0.732367893713227 0.732367893713227
3.24 0.75141609706171 0.75141524874832 0.751416088683921 0.751416088683921
3.32 0.77010823010838 0.77010738168467 0.770108221696074 0.770108221696074
3.40 0.78845736880808 0.78845652028376 0.788457360364270 0.788457360364270
3.48 0.80647587433955 0.80647502572333 0.806475865866949 0.806475865866949
3.56 0.82417545146531 0.82417460276501 0.824175442966349 0.824175442966349
3.64 0.84156719420135 0.84156634542400 0.841567185678219 0.841567185678219
3.72 0.85866162758285 0.85866077873478 0.858661619037519 0.858661619037519
3.80 0.87546874591965 0.87546789700658 0.875468737353900 0.875468737353900
3.88 0.89199804788966 0.89199719891678 0.891998039305110 0.891998039305110
3.96 0.90825856877877 0.90825771975076 0.908258560176891 0.908258560176891
4.04 0.92425891014122 0.92425806106235 0.924258901523332 0.924258901523332
4.12 0.94000726712415 0.94000641799821 0.940007258491471 0.940007258491471
4.20 0.95551145367381 0.95551060450466 0.955511445027437 0.955511445027436
4.28 0.97077892581729 0.97077807660683 0.970778917158225 0.970778917158225
4.36 0.98581680319361 0.98581595394963 0.985816794522765 0.985816794522765
4.44 1.00063188898968 1.00063103969670 1.000631880307906 1.000631880307906
4.52 1.01523068842100 1.01522983914930 1.015230679729059 1.015230679729059
4.60 1.02961942588257 1.02961857638119 1.029619417181158 1.029619417181158
4.68 1.04380406088334 1.04380321209931 1.043804052173115 1.043804052173115
4.76 1.05779030286630 1.05778945127489 1.057790294147855 1.057790294147855
4.84 1.07158362500631 1.07158278377077 1.071583616280190 1.071583616280190
4.92 1.08518927706926 1.08518839707176 1.085189268335969 1.085189268335969
5.00 1.09861229740415 1.09861156196633 1.098612288668110 1.098612288668110