一类基于幂级数的高精度修正牛顿法,用于求解非线性模型

O Ogbereyivwe, S. S. Umar
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引用次数: 0

摘要

本手稿提出了获取非线性模型解的高精度方法。该方法使用牛顿法作为预测器,并使用涉及扰动牛顿法的迭代函数和两个幂级数的商作为校正函数。收敛性理论分析表明,该方法的收敛阶数为四阶,每个循环需要对三个函数进行评估。与一些现有方法的计算性能比较表明,所开发的方法类具有完美的精度。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A class of power series based modified newton method with high precision for solving nonlinear models
This manuscript proposed high-precision methods for obtaining solutions for nonlinear models. The method uses the Newton method as its predictor and an iterative function that involves the perturbed Newton method with the quotient of two power series as the corrector function. The theoretical analysis of convergence indicates that the methods class is of convergence order four, requiring three functions evaluation per cycle. The computation performance comparison with some existing methods shows that the developed methods class has perfect precision.
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