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The present paper computationally examines the w-shaped solitary wave solutions for an important type of nonlinear Schrödinger equation that appeared in 1979 called the Chen-Lee-Liu (CLL) equation by proposing two recursive schemes. The schemes are based on the famous Adomian’s efficient decomposition technique. We successfully simulated the two proposed schemes with the aid of mathematical software and established a comparative analysis. It is noted from the present study that the improved method performs better than the classical method at different time levels. This is in fact in conformity with most of the results in the related literature. We finally present tables and a series of figures to support the presented results.

Numerical investigation of the Adomian-based methods with w-shaped optical solitons of Chen-Lee-Liu equation