In this paper, we solve chiral nonlinear Schrodinger equation (CNSE) numerically.\nTwo numerical methods are derived using the explicit Runge-Kutta\nmethod of order four and the linear multistep method (Predictor-Corrector\nmethod of fourth order). The resulting schemes of fourth order accuracy in\nspatial and temporal directions. The CNSE is non-integrable and has two\nkinds of soliton solutions: bright and dark soliton. The exact solutions and\nthe conserved quantities of CNSE are used to display the efficiency and robustness\nof the numerical methods we derived. Interaction of two bright solitons\nfor different parameters is also displayed.
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