Analytical approximations of three-point generalized Thomas–Fermi and Lane–Emden–Fowler type equations

In this work, we study multi-point singular boundary value problems (BVPs) that received considerable interest in various scientific and engineering applications. We focus this study on obtaining approximate solutions, particularly of the three-point generalized Thomas–Fermi and Lane–Emden–Fowler BVPs. Our algorithm employs two main steps. We first convert the three-point generalized Thomas–Fermi BVP to an equivalent integral equation, which overcomes the singularity behavior at the origin. We next apply the powerful decomposition method to the resulting integral equation. The decomposition method approximates the solution in a rapidly convergent series with easily computable components. In addition, sufficient theorems are supplied to confirm the uniqueness of the resolution of the problem. Finally, we examine the convergence analysis of the proposed method. Several examples are included to show the accuracy, applicability and power of the employed technique.