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Approximate solution of singular IVPs of Lane–Emden type and error estimation via advanced Adomian decomposition method
Journal of Applied Mathematics and Computing ( IF 2.2 ) Pub Date : 2020-10-24 , DOI: 10.1007/s12190-020-01444-2
Umesh , Manoj Kumar

This article aims to present a simple and effective method, named as advanced Adomian decomposition method, to attain the approximate solution of singular initial value problems of Lane–Emden type. Also, convergence analysis and error analysis with an upper bound of the absolute error for the proposed method are discussed. The proposed method is capable to remove the singular behaviour of the problems and provides an approximate solution up to the desired order. To illustrate the reliability and validity of the proposed method with error estimate several examples that arise in applications are considered and the attained outcomes are compared with some existing numerical methods.



中文翻译:

Lane-Emden型奇异IVP的近似解和通过高级Adomian分解方法的误差估计

本文旨在提出一种简单有效的方法,称为高级Adomian分解方法,以获得Lane-Emden型奇异初值问题的近似解。此外,讨论了所提出方法的收敛性分析和绝对误差上限的误差分析。所提出的方法能够消除问题的奇异行为,并提供直至所需阶数的近似解。为了说明带有误差估计的方法的可靠性和有效性,考虑了应用中出现的几个例子,并将获得的结果与一些现有的数值方法进行了比较。

更新日期:2020-10-30
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