Table 1 Comparative numerical results of \(f^{\prime\prime}\left( 0 \right)\) with^50,51,52 when \(M = 0 = Nr = \lambda = Nc = E = 0 = Pe = Lb = 0 = Bi = 0.\)

\(\lambda^{*}\)	\(\beta = 0.0\) ⁵⁰	\(\beta = 0.0\) RK-4 method⁵¹	\(\beta = 0.0\) Current results	\(\beta = 5.0\) ⁵⁰	\(\beta = 5.0\) ⁵²	\(\beta = 5.0\) Current results
0.01	0.009996	0.009999	0.009999	0.00902	0.009906	0.009905
0.02	0.019927	0.019924	0.019925	0.019561	0.019558	0.019557
0.05	0.049242	0.049246	0.049245	0.047082	0.047088	0.047088
0.10	0.096640	0.096638	0.096638	0.088783	0.088784	0.088784
0.20	0.186041	0.18643	0.18642	0.159723	0.159720	0.159720
0.50	0.414730	0.414732	0.414732	0.311099	0.311098	0.311099
1.0	0.687616	0.687612	0.687615	0.465619	0.465616	0.465618
2.0	0.97046	0.97048	0.97048	0.640374	0.640372	0.640371
5.0	1.211823	1.211820	1.211820	0.872404	0.872403	0.872405
10.0	1.275871	1.275870	1.275871	1.024092	1.0224090	1.0224090

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