Twelfth degree spline with application to quadrature

Mohammed, P. O.; Hamasalh, F. K.

doi:10.1186/s40064-016-3711-2

SpringerPlus

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

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