Large Time-Stepping Spectral Methods for the Semiclassical Limit of the Defocusing Nonlinear Schrödinger Equation

Table 2

Numerical errors obtained by using the BD1/EP1, BD2/EP2, and BD3/EP3 with 𝜆=𝜀=0.0025 and 𝑁=256.

𝐴	Δ𝑡	BD1/EP1	BD2/EP2	BD3/EP3
𝐴=0	Δ𝑡=0.01	0.498𝐸−2	unstable	unstable
	Δ𝑡=0.005	0.25𝐸−2	0.86𝐸−4	unstable
	Δ𝑡=0.0025	0.13𝐸−2	0.26𝐸−4	unstable
	Δ𝑡=0.00125	0.70𝐸−3	0.71𝐸−5	unstable
𝐴=0.1	Δ𝑡=0.01	0.23𝐸−2	0.35𝐸−3	unstable
	Δ𝑡=0.005	0.13𝐸−2	0.97𝐸−4	unstable
	Δ𝑡=0.0025	0.71𝐸−3	0.27𝐸−4	0.23𝐸−5
	Δ𝑡=0.00125	0.38𝐸−3	0.76𝐸−5	0.36𝐸−6
𝐴=0.5	Δ𝑡=0.01	0.57𝐸−2	0.41𝐸−3	0.31𝐸−3
	Δ𝑡=0.05	0.29𝐸−2	0.12𝐸−3	0.47𝐸−4
	Δ𝑡=0.0025	0.15𝐸−2	0.34𝐸−4	0.71𝐸−5
	Δ𝑡=0.00125	0.77𝐸−3	0.87𝐸−5	0.98𝐸−6