On a bivariate spectral relaxation method for unsteady magneto-hydrodynamic flow in porous media

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Table 1 Values of \(f''(0,\xi )\), \(g''(0,\xi )\), \(\theta '(0,\xi )\) and \(\phi '(0,\xi )\) when \(\lambda = 0.5, M = 2, c = 0.5, Sc = \gamma = 1, Pr = 1.5\)

\(\xi \)	BI-SRM	SRM	SQLM	Keller-box
\(\xi \)	(\(N_t = 10\))	(\(N_t = 2000\))	(\(N_t = 2000\))	(\(N_t = 2000\))
	\( f''(0,\xi )\)
0.1	−0.851257	−0.851257	−0.851257	−0.851257
0.3	−1.316705	−1.316705	−1.316705	−1.316705
0.5	−1.685306	−1.685306	−1.685306	−1.685306
0.7	−1.992608	−1.992608	−1.992608	−1.992608
0.9	−2.259335	−2.259335	−2.259335	−2.259335
	\( g''(0,\xi )\)
0.1	−0.417150	−0.417150	−0.417150	−0.417150
0.3	−0.639602	−0.639602	−0.639602	−0.639602
0.5	−0.817649	−0.817649	−0.817649	−0.817649
0.7	−0.966603	−0.966603	−0.966603	−0.966603
0.9	−1.095983	−1.095983	−1.095983	−1.095983
	\( \theta '(0,\xi )\)
0.1	−0.710882	−0.710882	−0.710882	−0.710882
0.3	−0.742842	−0.742842	−0.742842	−0.742842
0.5	−0.765244	−0.765244	−0.765244	−0.765244
0.7	−0.777270	−0.777270	−0.777270	−0.777270
0.9	−0.770807	−0.770807	−0.770807	−0.770807
	\( \phi '(0,\xi )\)
0.1	−0.634443	−0.634443	−0.634443	−0.634443
0.3	−0.766867	−0.766867	−0.766867	−0.766867
0.5	−0.891207	−0.891207	−0.891207	−0.891207
0.7	−1.010045	−1.010045	−1.010045	−1.010045
0.9	−1.125549	−1.125549	−1.125549	−1.125549
CPU time	0.47	18.90	83.24	900.30