Computational assessment of external force acting on beam elastic foundation

In this paper, we study some numerical methods to solve problems arising in applied sciences and engineering, primarily in beam theory. The problems of a beam on elastic foundation are usually describe with ill-posed fourth-order ordinary differential equations (ODEs). We study and formulate algorithms to aid the computation of the Exponentially Fitted Collocation Algorithm (EFCA), Hybrid Block Method (HBM), Homotopy Perturbation Algorithm (HPA), and Differential Transformation Algorithm (DTA) for the numerical solution of the ill-posed fourth-order ODEs. The formulated algorithms are further used for numerical comparison of the results. The results show that the algorithms are efficient, and numerical methods prove to be highly effective for solving beam problems.