Solutions of ordinary differential equations using accelerated genetic algorithm
Eman Ali Hussain, Yaseen Merzah Alrajhi · 2014
In this paper, introduced an accelerated method of Genetic Algorithms (GAs) to solve ordinary differential equations. Genetic Algorithm (GAs) is an optimization method we can use to find an explicit approximation for many ODEs with or without analytical closed form solution. We will look at how to implement a genetic program to approximate solutions to ODEs with and without analytical closed-form solutions. An accelerated method for solving ordinary differential equations, based on grammatical evolution is presented. The method forms generations of trial solutions expressed in an analytical closed form depending upon boundary conditions of the problem , particular solution, and exact solution (if exist) . 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.