Solving Poisson Equation by Genetic Algorithms

TL;DR

This paper presents a genetic algorithm-based method using grammatical evolution to solve Poisson equations, effectively recovering exact solutions or providing accurate approximations when analytical forms are unavailable.

Contribution

It introduces a novel approach combining genetic algorithms and grammatical evolution for solving Poisson equations, capable of exact or approximate solutions.

Findings

Most tested cases recover exact solutions

Method provides satisfactory approximations when exact solutions are not expressible

Effective for various Poisson equation examples

Abstract

This paper deals with a method for solving Poisson Equation (PE) based on genetic algorithms and grammatical evolution. The method forms generations of solutions expressed in an analytical form. Several examples of PE are tested and in most cases the exact solution is recovered. But, when the solution cannot be expressed in an analytical form, our method produces a satisfactory solution with a good level of accuracy