In this paper, the role of mathematical modeling in the development of clean technology has been considered.
One method each for obtaining approximate solutions of mathematical models by ordinary differential equations
and partial differential equations respectively arising from the modeling of systems and physical phenomena has
been considered. The construction of continuous hybrid methods for the numerical approximation of the solutions
of initial value problems of ordinary differential equations as well as homotopy analysis method, an approximate
analytical method, for the solution of nonlinear partial differential equations are discussed
