In this paper we import a novel approach to solve the non-linear fourth order boundary value problem. The basic strategy depends on integral operator equation which includes Green’s function and fixed point iteration. To ensure the method, three illustrations were conferred. From the residual or absolute error calculations, it is shown that the S-iteration for contraction operator gives fast convergence than Krasnoselskii–Mann’s iteration.

中文翻译：

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用S-迭代法求解非线性边值问题

在本文中，我们引入了一种新颖的方法来解决非线性四阶边值问题。基本策略取决于积分算子方程，其中包括格林函数和定点迭代。为了确保该方法，给出了三个插图。从残差或绝对误差计算中可以看出，收缩算子的S迭代比Krasnoselskii–Mann的迭代具有更快的收敛性。