Numerical Solutions of a Class of Fourth-Order Non-Linear Equations for Singular Boundary Value Problems

In this article, we investigate the numerical approximation of solutions to a class of fourth-order singular boundary value problems subject to various boundary conditions. The difficulty of the problem stems from its nonlinear, non-self-adjoint, and singular nature, along with the absence of closed-form solutions, which complicates analytical treatment. Moreover, the presence of dual solutions further challenges the construction of accurate approximations using standard discrete methods. To overcome these issues, we develop an iterative technique with the help of governing problem and the boundary conditions. We then show that the resulting numerical approximations converge to the exact solution. Several numerical examples are presented to demonstrate the accuracy, effectiveness, and broad applicability of the proposed method.