Abstract In this research, we present an iterative spectral method for the approximate solution of a class of Lane–Emden equations. In this procedure, we initially extend the Legendre wavelet which is appropriate for any time interval. Thereafter, the Guass-Legendre collection points of the Legendre wavelet are acquired. Employing this new approach, the iterative spectral technique converts the differential equation to a set of algebraic equations which diminishes the computational costs effectively. By solving the obtained algebraic equations, an accurate approximate solution for the assumed Lane–Emden equation is achieved. The present technique is validated by solving a number of Lane–Emden problems and are compared with other existing methods. The numerical simulations demonstrate that the new algorithm is simple and it has highly accuracy.

中文翻译：

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一种基于勒让德小波谱技术的求解Lane-Emden方程的新算法

摘要 在这项研究中，我们提出了一类Lane-Emden 方程近似解的迭代谱方法。在这个过程中，我们最初扩展了适用于任何时间间隔的勒让德小波。之后，得到Legendre小波的Guass-Legendre集合点。采用这种新方法，迭代谱技术将微分方程转换为一组代数方程，从而有效地降低了计算成本。通过求解所获得的代数方程，可以得到假设的 Lane-Emden 方程的精确近似解。本技术通过解决许多 Lane-Emden 问题得到验证，并与其他现有方法进行比较。数值模拟表明，新算法简单，精度高。