A Numerical Treatment of Nondimensional Form of Water Quality Model in a Nonuniform Flow Stream Using Saulyev Scheme

Table 5

The stability of FTCS and Saulyev schemes, 𝛾=max{𝛾^𝑛_𝑖∶1≤𝑖≤𝑀,0≤𝑛≤𝑁−1}.

Δ𝑥	Δ𝑡	𝜆	𝛾	FTCS scheme	Saulyev scheme
0.0125	0.010000	3.2	1.0665	Unstable	Stable
	0.005000	1.6	0.5332	Unstable	Stable
	0.002500	0.8	0.2667	Unstable	Stable
	0.001250	0.4	0.1333	Stable	Stable
	0.000625	0.2	0.0080	Stable	Stable
0.0125	0.010000	3.2	1.0665	Unstable	Stable
	0.005000	1.6	0.5332	Unstable	Stable
	0.002500	0.8	0.2667	Unstable	Stable
	0.001250	0.4	0.1333	Stable	Stable
	0.000625	0.2	0.0080	Stable	Stable
0.0125	0.010000	3.2	1.0665	Unstable	Stable
	0.005000	1.6	0.5332	Unstable	Stable
	0.002500	0.8	0.2667	Unstable	Stable
	0.001250	0.4	0.1333	Stable	Stable
	0.000625	0.2	0.0080	Stable	Stable