用数值微分法求解非线性方程的合适空间检测方法

S. Mughal, S. F. Shah, M. S. Chandio
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引用次数: 0

摘要

本文给出了用数值微分法求解非线性方程的一种新方法。在整个研究过程中,提出了一种迭代算法来寻找非线性方程的合适空间(根所在的位置),数值结果发现,该算法比二分法和Newton Raphson法需要更少的迭代次数来获得所需的精度。因此,可以说改进的方法比平分法和Newton Raphson法更快。为了比较结果,文中还举了一些与代数、三角和超越函数有关的例子。利用MATLAB、c++和MICROSOFT EXCEL软件对非线性方程求根求结果,并给出图形化表示。与已有的迭代法相比,改进后的方法执行效果更好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Suitable Space Detecting Method for solving non-linear equations by using Numerical Differentiation
This paper demonstrates a new method for solving a non-linear equation by using Numerical Differentiation. Throughout the studyan iterative algorithm has been proposed to find the suitable space (where root is located) for non-linear equations and it has been discovered by numerical results that proposed algorithm needs lesser number of iterations than Bisection method and Newton Raphson method to get required accuracy. Therefore, it can be said that modified method is faster than Bisection method and Newton Raphson method. In order to compare the results, some examples have been taken related to algebraic, trigonometric and transcendental functions. The software MATLAB, C++ and MICROSOFT EXCEL are used for finding the roots and results of non-linear equations with their graphical representation. It has been discovered that modified method executes better in comparison with existing iterative method.
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