Starting from the problem of the steady radial plasma transport in tokamak devices with divertor, we discuss a numerical method for solving a two-point boundary value problem by directly integrating nonlinear ordinary differential equations. The problem in question is reduced to one of solving a set of nonlinear equations by expanding their integral formal solution in terms of a set of orthogonal functions. When the cosine functions are taken to be.orthogonal funtions, special techniques are presented for numerical calculations of the multiple integrals with single variable limit and for solving transcendental equations whose root covers a wide range and for numerically solving systems of nonlinear equations. These techniques make our method more economical of computation. The method offered can, at least in principle, be extended to solve other two-point boundary value problems of the same class.