Arabian Journal of Mathematics Pub Date : 2021-05-01 , DOI: 10.1007/s40065-021-00323-3 Manoj Kumar Singh , Arvind K. Singh
The motive of the present work is to introduce and investigate the quadratically convergent Newton’s like method for solving the non-linear equations. We have studied some new properties of a Newton’s like method with examples and obtained a derivative-free globally convergent Newton’s like method using forward difference operator and bisection method. Finally, we have used various numerical test functions along with their fractal patterns to show the utility of the proposed method. These patterns support the numerical results and explain the compactness regarding the convergence, divergence and stability of the methods to different roots.
中文翻译:
无导数的全局收敛方法及其变形
本工作的目的是介绍和研究求解非线性方程的二次收敛牛顿法。我们通过实例研究了牛顿类方法的一些新性质,并使用前向差分算子和二等分方法获得了无导数的全局收敛牛顿类方法。最后,我们使用了各种数值测试函数及其分形模式来证明所提出方法的实用性。这些模式支持数值结果,并解释了方法对于不同根的收敛性,发散性和稳定性的紧凑性。