Two New Iterative Methods for Solving Nonlinear Equations without Derivative
Keywords:
Non-linear Equations, Order of Convergence, Derivative Free MethodAbstract
In this paper, we propose two new iterative methods for solving nonlinear equations with one variable without derivative. In convergence theory, the two new iterative methods have second and third order convergence. Some numerical experiments show that the two new derivative free iterative methods outperform the several other existing methods.
References
Argyros, I.K. (2008). Convergence and Application of Newton-Type Iteration. Newyork: Springer.
Conte, S.D., & Boor Carl de. (1981). An Algorithmic Approach. Elementary Numerical Analysis. McGraw-Hill.
Dehghan, M., & Hajarian, M. (2010). Some derivative free quadratic and cubic convergence iterative formulars for solving nonlinear
equations. Computational and Applied Mathematics, 29, 19-30.
Hafiz, M.A. (2014). Solving Nonlinear Equations Using Steffensen-Type Methods With Optimal Order of Convergence. Palestine Journal of
Mathematics, 3(1), 113-119.
Jain, P. (2007). Steffensen type methods for solving non-linear equations. Appl. Math. Comput.,194, 527-533.
Jaiswal, J.P. (2013). A New Third-Order Derivative Free method for Solving Nonlinear Equations. Universal Journal of Applied Mathematics,
(2), 131-135.
Qian, Y.H., & Guo, Q.W. (2016). A new derivative-free iterative method for solving nonlinear equations. Nonlinear Sci.Lett. A, 7(2), 32-40.
Sharma, J.R. (2005). A composite third order Newton Steffensen method for solving nonlinear equations. Appl. Math. Comput., 169
(1), 242-246.
Singh, B. (2017). Fourth-order Steffensen type methods for nonlinear equations. International Journal of Statistics and Applied Mathematics,
(4), 11-15.