In this article, an effective computational scheme is introduced to obtain the approximate analytical solutions of a class of two-point nonlinear singular boundary value problems arising in different physical models. The proposed approach consists of two steps. First, construct an integral operator by introducing Green's function, and then, the Halpern fixed point iterative scheme is applied to this integral operator to construct the iterative technique. The convergence of the introduced method is also discussed. To exhibit the efficiency of the method, we consider various numerical examples. The main advantages of the proposed method over existing methods are that the proposed method does not require Adomian polynomials to handle the nonlinearity, solves the problem without using the Lagrange multipliers and constrained variations and takes both endpoints of the interval into consideration. Further, the proposed method tackles the problems without requiring linearization, discretization, and perturbation assumptions unlike other semi-analytical methods.

本文介绍了一种有效的计算方案，以获得在不同物理模型中产生的一类两点非线性奇异边值问题的近似解析解。提议的方法包括两个步骤。首先，通过引入格林函数构造积分算子，然后将Halpern不动点迭代方案应用于该积分算子，以构造迭代技术。还讨论了所引入方法的收敛性。为了展示该方法的效率，我们考虑各种数值示例。与现有方法相比，该方法的主要优势在于，该方法不需要Adomian多项式来处理非线性，在不使用拉格朗日乘数和约束变量的情况下解决了问题，并考虑了区间的两个端点。此外，与其他半分析方法不同，所提出的方法无需线性化，离散化和微扰假设即可解决问题。