One-dimensional steady-state diffusion equations with nonlinear rate expressions are a feature of the study of biological systems. These differential equations are usually characterized by two point boundary conditions. The exact analytical solutions of these equations exist in certain special cases; moreover, the asymptotic solutions, where they exist, approach the numerical solutions, for a very limited range of the parameters involved. The transformation of these equations to initial value problems is of limited utility and cannot be applied for known values of the parameters. For numerical solutions, an iterative scheme has been introduced to satisfy the boundary conditions. This scheme employs the Newton-Raphson Method. A single suitably selected initial value is sufficient to satisfy the bound-ary conditions for all given values of the parameter. The method has been sub-stantiated with the help of examples and computer-based algorithm, and its flow chart is given.