Chebyshev finite difference method for solving a mathematical model arising in wastewater treatment plants

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.

Keywords:

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