Solution of differential equations with Genetic Programming and the Stochastic Bernstein Interpolation

This report introduces a method for the solution of the Convection-Diffusion equations (CDE) that combines Genetic Programming with Stochastic Bernstein Interpolation. Significantly, it is being used to solve a problem that has resisted analysis for a long time using other methods. Although the method in this report solves the one-dimensional CDE which has also been solved analytically and optimally, our strategy of combining the Stochastic Bernstein Interpolation method with GP allows for the method to extend to higher dimensions, and thus it shows how to construct GP based methods for solving a range of computational problems in multiple dimensions which have hitherto resisted numerical solution.