Homotopy Analysis-Based Hybrid Genetic Algorithm and Secant Method to Solve IVP and Higher-Order BVP

The analytical solution of the Initial Value Problem (IVP) and Boundary (BVP) is an essential issue in numerous engineering applications. However, it cannot usually be realized by simple methods. Accordingly, utilizing semi-analytical methods such as homotopy analysis method (HAM) alternative. depends on calculating a dedicated convergence parameter. Different algorithms were proposed to realize this Thus, converting residual function into optimization problem represented promising solution. resulted can solved either using traditional or meta-heuristic algorithms. In paper, new algorithm called Homotopy Analysis Method-based hybrid Genetic Secant (HAMGS) for solving problems. hybridization based crossover process genetic improve accelerate convergence. Moreover, will protect secant from divergence searching individuals. As result, control parameter detected algebraically without drawing h-curves. This facilitates identifying minimum number HAM terms reach solution, which reduces computational burden remarkably. presumed improvement pairing improving solver verified via four IVPs three higher-order BVPs. results corroborate competence its ability solve problems efficiently.