Table 3.

Numerical and analytical results for the values of $R{e}_t$, $\beta =0.021942857$ and $n=7$.

Reynolds no. ${\mathrm{R}\mathrm{e}}_t$	The value of k or $\beta {\mathrm{R}\mathrm{e}}_t^{\frac{n-2}{n}}$ for $n=7$ $\beta =0.021942857$	Numerical solution of $u^{″}\left(0\right)$
5000	9.6253	1.5399
10,000	15.792	1.9724
20,000	25.9094	2.5264
30,000	34.6128	2.9201
40,000	42.5088	3.2361
50,000	49.854	3.5045
60,000	56.7882	3.7403
70,000	63.3983	3.952
80,000	69.7429	4.145
90,000	75.8644	4.3231
100,000	81.7941	4.4889
110,000	87.5564	4.6443
120,000	93.1708	4.7909
130,000	98.6529	4.9298
140,000	104.0157	5.0621
150,000	109.2701	5.1883
160,000	114.4252	5.3093
170,000	119.4891	5.4255
180,000	124.4684	5.5374
190,000	129.3694	5.6454
200,000	134.1971	5.7498
210,000	138.9563	5.8508
220,000	143.6512	5.9488
230,000	148.2855	6.044
240,000	152.8625	6.1366
250,000	157.3854	6.2267
260,000	161.8569	6.3146
270,000	166.2795	6.4002
280,000	170.6555	6.4839
290,000	174.9870	6.5657
291,000	175.4178	6.5738
292,000	175.8482	6.5818
293,000	176.2781	6.5899
294,000	176.7077	6.5979
295,000	177.1368	6.6059
296,000	177.5655	6.6139
297,000	177.9938	6.6219
298,000	178.4216	6.6298
299,000	178.8491	6.6378
299,200	178.9345	6.6393
299,355	179.0007	6.6406
299,360	179.0029	6.6406
299,365	179.0050	6.6406
299,370	179.0071	6.6407
299,371	179.0076	6.6407
299,372	179.008	6.6407
299,373	179.0084	−0.7512
299,374	179.0089	−0.7512
299,375	179.0093	−0.7512
299,380	179.0114	−0.7512
299,600	179.1054	−0.7514
300,000	179.2761	−0.7518
310,000	183.5246	−0.7607
310,500	183.736	−0.7611
310,550	183.7571	−0.7611
310,560	183.7613	−0.7611
310,564	183.763	−0.7611
310,565	183.7634	0
310,700	183.8205	0
310,840	183.8797	0
310,850	183.8797	0
350,000	200.1436	0
400,000	220.1732	0