Spectral Relaxation Method and Spectral Quasilinearization Method for Solving Unsteady Boundary Layer Flow Problems

Table 5

Comparison between the SRM and Keller-Box approximate numerical values for 𝑓^′′(0,𝜉 ), 𝑔^′′(0,𝜉), 𝜃^′(0,𝜉), and 𝜙^′(0,𝜉) when 𝜆=0.5, 𝑀=2, 𝑐=0.5, Sc=𝛾=1, and Pr=1.5 in Example 2.

	Spectral quasilinearisation method				Keller-Box
𝜉⧵Δ𝜉	0.01	0.002	0.001	0.0005	0.0005
	𝑓^′′(0,𝜉)
0.1	−0.851309	−0.851259	−0.851258	−0.851257	−0.851257
0.3	−1.316738	−1.316706	−1.316705	−1.316705	−1.316705
0.5	−1.685327	−1.685307	−1.685306	−1.685306	−1.685306
0.7	−1.992622	−1.992609	−1.992608	−1.992608	−1.992608
0.9	−2.259344	−2.259335	−2.259335	−2.259335	−2.259335
	𝑔^′′(0,𝜉)
0.1	−0.417173	−0.417151	−0.417151	−0.417150	−0.417150
0.3	−0.639617	−0.639603	−0.639602	−0.639602	−0.639602
0.5	−0.817659	−0.817649	−0.817649	−0.817649	−0.817649
0.7	−0.966610	−0.966604	−0.966603	−0.966603	−0.966604
0.9	−1.095987	−1.095983	−1.095983	−1.095983	−1.095983
	𝜃^′(0,𝜉)
0.1	−0.710885	−0.710882	−0.710882	−0.710882	−0.710882
0.3	−0.742845	−0.742842	−0.742842	−0.742842	−0.742843
0.5	−0.765247	−0.765244	−0.765244	−0.765244	−0.765244
0.7	−0.777274	−0.777270	−0.777270	−0.777270	−0.777270
0.9	−0.770819	−0.770807	−0.770807	−0.770807	−0.770807
	𝜙^′(0,𝜉)
0.1	−0.634447	−0.634443	−0.634443	−0.634443	−0.634444
0.3	−0.766870	−0.766867	−0.766867	−0.766867	−0.766867
0.5	−0.891209	−0.891207	−0.891207	−0.891207	−0.891207
0.7	−1.010046	−1.010045	−1.010045	−1.010045	−1.010045
0.9	−1.125550	−1.125549	−1.125549	−1.125549	−1.125549