E. Sokhanvar - Department of Mathematics, Kerman Graduate University of Technology, Mahan, Kerman, Iran
S. yousefi - Shahid Beheshti University

Pollution has become a very serious threat to our environment. Monitoring pollution is the rst step toward planning to save the environment. The use of dierential equations, monitoring pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve non-linear oscillatory systems such as modelling the pollution of a system of lakes. The method is based upon Bernoulli polynomials. These polynomials are rst presented. The Bernoulli Ritz-collocation method is then utilized to reduce modelling the pollution of a system of lakes to the solution of algebraic equations. An illustrative example is included to demonstrate the validity and applicability of the proposed method.

Bernoulli polynomials, Modelling the pollution of a system of lakes, Ritz-collocation method