The Bernoulli Ritz-collocation method to the solution of modelling the pollution of a system of lakes

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 di erential equations, monitor- ing pollution has become possible. In this paper, a Ritz-collocation method is introduced to solve modelling the pollution of a system of lakes by a system of di erential equations. 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 alge- braic equations. An illustrative example is included to demonstrate the validity and applicability of the proposed method.