On Extending the Quasilinearization Method to Higher Order Convergent Hybrid Schemes Using the Spectral Homotopy Analysis Method

Table 1

Comparison between the computed values of the skin friction 𝑓^′′(0) for the Blasius flow (𝛽=1/2,𝛽₁=0).

iter.	𝑓^′′(0)	Error
	SHAM
1	0.361245275076317576714175486031	0.02918793886112127777699542402
10	0.332060294018222201221920675183	0.00000295780302590228474061317
20	0.332057337274670714006530763206	0.00000000105947441506935070120
30	0.332057336215760109582560249181	0.00000000000056381064538018717
40	0.332057336215196653344046405966	0.00000000000000035440686634396
60	0.332057336215196298937262729762	0.00000000000000000000008266775
	Scheme-0
1	0.36124527510805664031836423508	0.02918793889286034138118417307
2	0.33293906079206190667160822082	0.00088172457686560773442815881
3	0.33205878995514977263006366166	0.00000145373995347369288359965
4	0.33205733621994973222724960736	0.00000000000475343329006954535
5	0.33205733621519629893723540415	0.00000000000000000000005534214
6	0.33205733621519629893718006201	0.00000000000000000000000000000
	Scheme-1
1	0.33849743020925601396026175681	0.00644009399405971502308169480
2	0.33205889444389263880627992358	0.00000155822869633986909986157
3	0.33205733621519633877777093517	0.00000000000000003984059087316
4	0.33205733621519629893718006201	0.00000000000000000000000000000
	Scheme-2
1	0.33398877527020321822942828158	0.00193143905500691929224821957
2	0.33205733679309573625968418056	0.00000000057789943732250411855
3	0.33205733621519629893718006201	0.00000000000000000000000000000
[29]: 0.33205733621519629893718006201 (104 iterations)