Summary: 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 differential 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 first 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.