一种合理的最优块混合方法提高了求解Lane-Emden方程的精度

Sandile Motsa , Salma Ahmedai , Mpho Nefale , Olumuyiwa Otegbeye
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引用次数: 0

摘要

本文介绍了一种分块混合方法,用于有效求解具有原点奇异性的二阶边值问题Lane-Emden方程。该方法通过合理逼近最优点,对网格点进行策略性选择,使局部截断误差最小化,从而提高解的精度。大量的数值实验表明,这种方法,以下称为理性最优块混合方法(ROBHM),比传统方法提供了更高的精度和收敛速度。分析强调了有理近似参数(表示为d)在优化精度和计算效率方面的关键作用。通过保持计算需求和解决方案质量之间的平衡,Rational最优块混合方法为解决复杂的微分方程开辟了新的途径,从而有助于推进以奇点为标志的边值问题的数值分析。
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A rational optimal block hybrid method for enhanced accuracy in solving Lane–Emden equations
This paper introduces a block hybrid method designed for the effective resolution of Lane–Emden equations, which are characterized as second-order boundary value problems incorporating a singularity at the origin. Utilizing a strategic selection of grid points through the rational approximation of optimal points, this method aims at minimizing local truncation errors, thereby enhancing the precision of solutions. Extensive numerical experimentation reveals that this approach, hereinafter referred to as the Rational Optimal Block Hybrid Method (ROBHM), offers improved accuracy and convergence rates over traditional methods. The analysis underscores the critical role of the rational approximation parameter (denoted as d) in optimizing both accuracy and computational efficiency. By maintaining a balance between computational demands and the quality of solutions, the Rational Optimal Block Hybrid Method opens new avenues for tackling complex differential equations, thus contributing to the advancement of numerical analysis of boundary value problems marked by singularities.
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CiteScore
6.20
自引率
0.00%
发文量
138
审稿时长
14 weeks
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