Solving nonlinear differential equations of membrane transport by orthogonal collocation

An efficient numerical technique, based on the “orthogonal collocation” method of weighted residuals, has been developed to solve the nonlinear differential equations of membrane transport models. This is a much faster and more precise method than the formerly used method of Runge—Kutta. An efficient numerical method is required when the model is coupled with a nonlinear parameter estimation routine which calls for the model to be solved many times. The numerical solution for velocity profiles inside the pores of reverse osmosis membranes has proven to be efficient and accurate. The technique has been validated. The velocity profiles in the membrane pores have been shown.