Application of Artificial Bee Colony Algorithm in Solving Second-Order Differential Equations

This paper presents the use of the Artificial Bee Colony (ABC) algorithm to solve second order initial value problems (IVPs). The numerical methods like RK4 and RK-Gill are not very efficient in terms of accuracy, versatility and computational time especially with large step sizes. Based on the foraging behavior of honey bees the ABC approach is capable of enhancing the search for solutions in the search space to achieve the best solution. In this paper we use the second order IVPs to test the performance of the ABC algorithm and compare it with the exact solution, RK4, and RK-Gill methods. The efficacy of the proposed ABC algorithm in terms of accuracy and comparison to other methods is shown in tables and heat maps with zero visible error on several datasets. This shows that the proposed method is accurate and consistent in providing numerical solutions free from rounding off errors. Furthermore, we investigate the combination of the ABC algorithm with conventional numerical techniques and state-of-the-art computing approaches including adaptive step size methods and parallel computing in order to enhance the solution quality and accuracy. The paper also examines how integrating the proposed ABC algorithm with intelligent and machine learning approaches can be useful in extending the possibilities of numerical methods for solving differential equations and demonstrates its versatility as a computational intelligence method for different applications.