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The nonlinear Schr\"odinger and the Schr\"odinger-Newton equations model manyphenomena in various fields. Here, we perform an extensive numerical comparisonbetween splitting methods (often employed to numerically solve these equations)and the integrating factor technique, also called Lawson method. Indeed, thelatter is known to perform very well for the nonlinear Schr\"odinger equation,but has not been thoroughly investigated for the Schr\"odinger-Newton equation.Comparisons are made in one and two spatial dimensions, exploring differentboundary conditions and parameters values. We show that for the short rangepotential of the nonlinear Schr\"odinger equation, the integrating factortechnique performs better than splitting algorithms, while, for the long rangepotential of the Schr\"odinger-Newton equation, it depends on the particularsystem considered.

Integrating factor techniques applied to the Schr\"odinger-like equations. Comparison with Split-Step methods