Applications of Genetic Programming and Automatic Differentiation Algorithms in the Solution of Ordinary and Partial Differential Equations
There is a significant number of research projects using differential equations to model important and complex problems of engineering and other scientific knowledge areas. This paper investigates the potential that computational algorithms have to determine analytical solutions for ordinary and partial differential equations. In order to do so, the evolutionary method of genetic programming and the automatic differentiation method are applied. Using the MatLab programming environment, several GPAD algorithms are developed and problems of distinct differential equations are addressed. The results are promising, with exact solutions obtained for most of the addressed equations, including ones that commercial systems could not find a symbolic solution to. The conclusion is that GPAD algorithms can be used to discover analytic solutions for ordinary differential equations and partial differential equations.
