The goal of our research is to evaluate the general methods of finding solution of a system of differential equations. In this paper we investigate a novel two step genetic algorithm approach that produces an analytical solution of the system. The evaluation of the algorithm reveals its capability to solve non-trivial systems in very small number of generations. In order to find the best solution, and due to the fact that the simulations are computational intensive, we use grid genetic algorithms. Using the gLite based Grid, we propose a grid genetic solution that uses large number of computational nodes, that archives excellent performance. This research will be the basis on our goal of solving more complex research problems based around the Schrodingers equation.