The Spectral Homotopy Analysis Method Extended to Systems of Partial Differential Equations

Table 1

Comparison of the SHAM solutions for 𝑓^′′(𝜉,0), −𝜃^′(𝜉,0), and −𝜙^′(𝜉,0) against those of the SQLM at different values of 𝜉.𝑀=𝐾=30, ℏ = −1, 𝐿=30, 𝑁=100, 𝜆=0.5, Pr=0.7, Nr=0.5, Le=3, Sc=1, 𝛼=1, and 𝜎=1.

𝜉	𝑓^′′(𝜉,0)		−𝜃^′(𝜉,0)		−𝜙^′(𝜉,0)
	SHAM	SQLM	SHAM	SQLM	SHAM	SQLM
0.1	−0.540183	−0.540183	0.475790	0.475790	0.993124	0.993124
0.2	−0.516888	−0.516888	0.479891	0.479891	1.010491	1.010491
0.3	−0.494398	−0.494398	0.484385	0.484385	1.029550	1.029550
0.4	−0.472821	−0.472821	0.489330	0.489330	1.050616	1.050616
0.5	−0.452295	−0.452295	0.494804	0.494804	1.074110	1.074110
0.6	−0.432994	−0.432994	0.500905	0.500905	1.100615	1.100615
0.7	−0.415145	−0.415145	0.507775	0.507775	1.130989	1.130989
0.8	−0.399066	−0.399066	0.515629	0.515629	1.166621	1.166621
0.9	−0.385221	−0.385221	0.524843	0.524843	1.210167	1.210167
1.0	−0.374286	−0.374286	0.536307	0.536307	1.268622	1.268622