In this article, we shall present a novel approach based on embedding Green's function into Ishikawa fixed point iterative procedure for the numerical solution of a broad class of boundary value problems of third order. A linear integral operator expressed in terms of Green's function is constructed, then the well-known Ishikawa fixed point iterative scheme is applied to obtain a new iterative scheme. The aim of our alternative strategy is to overcome the major deficiency of other iterative schemes that usually result in the deterioration of the error as the domain increases. Furthermore the proposed strategy will improve the rate of convergence of other existing methods that are based on Picard's and Mann's iterative schemes. Convergence results of the iterative algorithm have been proved. A number of numerical examples shall be solved to illustrate the method and demonstrate its reliability and accuracy. Moreover, we shall compare our results with both the analytical and the numerical solutions obtained by other methods that exist in the literature.

在本文中，我们将提出一种基于将格林函数嵌入 Ishikawa 不动点迭代程序的新方法，用于数值解一类广泛的三阶边值问题。构造了一个用格林函数表示的线性积分算子，然后应用著名的石川不动点迭代方案得到一个新的迭代方案。我们的替代策略的目的是克服其他迭代方案的主要缺陷，这些缺陷通常会随着域的增加而导致错误恶化。此外，所提出的策略将提高基于 Picard 和 Mann 迭代方案的其他现有方法的收敛速度。证明了迭代算法的收敛性。应解决一些数值例子来说明该方法并证明其可靠性和准确性。此外，我们将我们的结果与文献中存在的其他方法获得的解析解和数值解进行比较。