The aim of the present research is to solve a nonlinear system of second order two-point boundary value problem by using a rapid Adams technique as well as well–known explicit Runge-Kutta numerical scheme. The designed methodology of both the numerical schemes is also presented. Fourdifferent examples of the system of nonlinear two-point boundary value problems have been discussed and the numerical results obtained from the above mentioned two techniques have been compared with the exact solutions that depict the correctness of the model as well as the numerical schemes. The achieved result details of the system of two-point boundary value problems is presented in the form of tables as well as numerical configurations.