In this paper, we propose an efficient numerical technique based on the Bernstein polynomials for the numerical solution of the equivalent integral form of the derivative dependent Emden–Fowler boundary value problems which arises in various fields of applied mathematics, physical and chemical sciences. The Bernstein collocation method is used to convert the integral equation into a system of nonlinear equations. This system is then solved efficiently by suitable iterative method. The error analysis of the present method is discussed. The accuracy of the proposed method is examined by calculating the maximum absolute error and the $$L_{2}$$ error of four examples. The obtained numerical results are compared with the results obtained by the other known techniques.

中文翻译：

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使用 Bernstein 搭配方法求解具有导数相关性的 Emden-Fowler 边值问题的数值结果

在本文中，我们提出了一种基于 Bernstein 多项式的有效数值技术，用于求解应用数学、物理和化学科学各个领域中出现的导数相关 Emden-Fowler 边值问题的等效积分形式。Bernstein搭配法用于将积分方程转化为非线性方程组。然后通过合适的迭代方法有效地求解该系统。讨论了本方法的误差分析。通过计算四个例子的最大绝对误差和$$L_{2}$$误差来检验所提出方法的准确性。将获得的数值结果与通过其他已知技术获得的结果进行比较。