This project introduced an accelerated method of Genetic Algorithms (GAs) to solve Partial differential equations. This new method for solving partial differential equations, based on grammatical evolution is presented. The method forms generations of trial solutions expressed in an analytical closed form and developed by inserting the boundary conditions, part of exact solution or exact solution as a vectors of trial solutions in the population of the problem. Several examples are worked out and in most cases the exact solution is recovered. When the solution cannot be expressed in a closed analytical form then our method produces an approximation with a controlled level of accuracy. We report results on several problems to illustrate the potential of this approach.