- - - Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Kashan, Kashan ۸۷۳۱۷-۵۳۱۵۳, Iran
- - - Department of Chemical industries, Faculty of Valiasr, Tehran Branch, Technical and Vocational University (TVU), Tehran, Iran

The Chebyshev finite difference method is applied to solve a system of two coupled nonlinear Lane-Emden differential equations arising in mathematical modelling of the excess sludge production from wastewater treatment plants. This method is based on a combination of the useful properties of Chebyshev polynomials approximation and finite difference method. The approach consists of reducing the problem to a set of algebraic equations. Numerical results are included to demonstrate the validity and applicability of the technique and a comparison is made with the existing results.

Chebyshev finite difference method, Gauss-Lobatto nodes, Excess sludge production, Activated sludge, Carbon substrate