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.