On the Analytical and Numerical Solutions of the One-Dimensional Nonlinear Schrodinger Equation

Table 1

A sum of squares errors (SSEs) comparison of the Hopscotch method, the Crank-Nicolson method, the split-step Fourier transform, and the Fourier pseudospectral method at and over a space domain , computed over a range of different values from to .

Time,	SSE of Hopscotch method	SSE of Crank-Nicolson method	SSE of split-step Fourier transform	SSE of Fourier pseudospectral method
	4.8101e − 10	6.5687e − 07	2.5802e − 28	1.4118e − 04
	1.9241e − 09	2.6292e − 06	9.8438e − 28	5.6590e − 04
	4.3293e − 09	5.9195e − 06	1.9592e − 27	1.2759e − 03
	7.6967e − 09	1.053e − 05	3.4388e − 27	2.2730e − 03
	1.2026e − 08	1.6464e − 05	5.2826e − 27	5.1356e − 03
	1.7319e − 08	2.3724e − 05	7.4381e − 27	5.1356e − 03
	2.3573e − 08	3.2312e − 05	1.0108e − 26	7.0047e − 03
	4.8231e − 06	7.0135e − 03	2.0486e − 24	1.7160e + 00