A Metaheuristic Optimization Algorithm for Solving Higher-Order Boundary Value Problems

An effective metaheuristic algorithm to solve the higher-order boundary value problems, called a genetic programming technique, is presented. In this paper, a genetic programming algorithm, which depends on the syntax tree representation, is employed to obtain the analytical solutions of higher-order differential equations with the boundary conditions. The proposed algorithm can produce an exact or approximate solution when the classical methods lead to unsatisfactory results. To illustrate the efficiency and accuracy of the designed algorithm, several examples are tested. Finally, the obtained results are compared with the existing methods such as the homotopy analysis method, the B-Spline collocation method, and the differential transform method.