A method based on genetic programming to find symbolic solutions of differential equations

Abstract

In this study, a method based on Genetic Programming (GP) to solve differential equations was carried out. We first described the fundamentals of the GP method from its conceptual insights until its implementation in Python. Then we used the method to solve three problems in ODEs to illustrate some advantages and disadvantages from a computational and a mathematical point of view. The problems solved included an initial value problem, a nonlinear boundary value problem and a numerically unstable problem. Results show some advantages concerning the use of the method for non-linear and ill-conditioned problems and allow us to propose several questions for future research.