<p>This article builds upon our previous work, where we developed a numerical approach to solving quantum mechanical scattering problems using the phase function method. By employing the Runge-Kutta method to solve the non-linear phase equation derived from the time-independent Schrödinger equation, we modeled S-wave scattering phase shifts for neutron-proton (<i>np</i>) interactions using the Yukawa and Malfliet-Tjon potentials. In the present work, the model parameters for the Malfliet-Tjon (MT) potential have been determined using three-point analysis and global optimization. These parameters have been utilized to compute the scattering phase shifts for the triplet ³<i>S</i>₁ and singlet ¹<i>S</i>₀ states of <i>np</i>-scattering. Furthermore, the low-energy scattering parameters and the total S-wave cross-section have been calculated from these phase shifts, showing consistency with experimental data. In addition, the deuteron binding energy calculated using the ³<i>S</i>₁ MT potential obtained through global optimization is found to be (BE) = −2.1233659 MeV, which is very close to the experimental binding energy of the deuteron.</p>