Numerical study of oxygen and carbon substrate concentrations in excess sludge production using sinc-collocation method

Abstract

A numerical procedure is developed to obtain the solution of a mathematical model that relates the concentrations of carbon substrate and oxygen within a microbial floc particle. This model can be reduced to a system of two coupled nonlinear singular differential equations. Our approach is based on sinc-collocation method. Sinc based methods are characterized by exponentially decaying errors associated with their approximations. Also, approximation by sinc methods handles singularities in the problem. Properties of the sinc functions are utilized to reduce the computation of this model to systems of algebraic equations. The method is easy to implement and the results are compared with some well-known results which show that they are accurate.