An Efficient Numerical Method for the Solution of the Schrödinger Equation

Table 1

Coupled differential equations. Real time of computation (in seconds) (RTC) and maximum absolute error (MErr) to calculate for the variable step methods, Method I–Method X. . We note that is the maximum step size. indicates the number of equations of the set of coupled differential equations.

Method			RTC	MErr
Method I	4	0.014	3.25
	9	0.014	23.51
	16	0.014	99.15
Method II	4	0.056	1.55
	9	0.056	8.43
	16	0.056	43.32
Method III	4	0.007	45.15
	9
	16
Method IV	4	0.112	0.39
	9	0.112	3.48
	16	0.112	19.31
Method V	4	0.448	0.14
	9	0.448	1.37
	16	0.448	9.58
Method VI	4	0.448	0.09
	9	0.448	1.10
	16	0.448	8.57
Method VII	4	0.448	0.06
	9	0.448	1.04
	16	0.448	7.58
Method VIII	4	0.448	0.04
	9	0.448	1.02
	16	0.448	7.48
Method IX	4	0.448	0.04
	9	0.448	1.01
	16	0.448	7.15
Method X	4	0.896	0.02
	9	0.896	0.45
	16	0.896	6.11