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Analytic solution of system of singular nonlinear differential equations with Neumann-Robin boundary conditions arising in astrophysics
arXiv - CS - Numerical Analysis Pub Date : 2020-07-03 , DOI: arxiv-2007.01653
Randhir Singh

In this paper, we propose a new approach for the approximate analytic solution of system of Lane-Emden-Fowler type equations with Neumann-Robin boundary conditions. The algorithm is based on Green's function and the homotopy analysis method. This approach depends on constructing Green's function before establishing the recursive scheme for the approximate analytic solution of the equivalent system of integral equations. Unlike Adomian decomposition method (ADM) \cite{singh2020solving}, the present method contains adjustable parameters to control the convergence of the approximate series solution. Convergence and error estimation of the present is provided under quite general conditions. Several examples are considered to demonstrate the accuracy of the current algorithm. Computational results reveal that the proposed approach produces better results as compared to some existing iterative methods.

中文翻译:

天体物理学中具有Neumann-Robin边界条件的奇异非线性微分方程组的解析解

在本文中,我们提出了一种具有 Neumann-Robin 边界条件的 Lane-Emden-Fowler 型方程组的近似解析解的新方法。该算法基于格林函数和同伦分析方法。这种方法依赖于在建立积分方程等效系统近似解析解的递归格式之前构造格林函数。与 Adomian 分解方法 (ADM) \cite{singh2020solving} 不同,本方法包含可调节参数来控制近似级数解的收敛。目前的收敛和误差估计是在相当普遍的条件下提供的。考虑了几个例子来证明当前算法的准确性。
更新日期:2020-07-06
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