A GENETIC PROGRAMMING TECHNIQUE FOR SOLVING SYSTEMS OF DIFFERENTIAL EQUATIONS

摘要

The solution of differential equations is a topic of great interest to modelers of physical phenomenon. Popular numerical solution techniques such as the finite difference method provide solutions of sufficient accuracy but at a great time cost for large-scale problems. Current advances in Virtual Reality (VR) make it possible to envision that VR could be a new and interesting environment for engineering design. But for engineering design to operate in the required interactive manner, great advances need to occur in rapidly solving the differential equations that govern material behavior. Our method uses genetic programming techniques to find analytical functions that satisfy a given system of differential equations. The method employs automatically computed analytical derivatives of the candidate solution functions for higher accuracy and faster solution convergence.