  This paper is devoted to find the numerical solutions of one dimensional
general nonlinear system of third-order boundary value problems (BVPs) for the
pair of functions using Galerkin weighted residual method. We derive
mathematical formulations in matrix form, in details, by exploiting Bernstein
polynomials as basis functions. A reasonable accuracy is found when the
proposed method is used on few examples. At the end of the study, a comparison
is made between the approximate and exact solutions, and also with the
solutions of the existing methods. Our results converge monotonically to the
exact solutions. In addition, we show that the the derived formulations may be
applicable by reducing higher order complicated BVP into a lower order system
of BVPs, and the performance of the numerical solutions is satisfactory.
