论文信息 - On the Higher-Order Method for the Solution of a Nonlinear Scalar Equation

On the Higher-Order Method for the Solution of a Nonlinear Scalar Equation

In this paper, a higher-order method for the solution of a nonlinear scalar equation is presented. It is proved that the new method is locally convergent with an order of (m+2), where m is the highest order derivative used in the iterative formula. Some numerical examples are used to demonstrate the new method.

Min Chen | Tsu-Shuan Chang

[1] J. Traub. Iterative Methods for the Solution of Equations , 1982 .

[2] F. Potra,et al. Nondiscrete induction and iterative processes , 1984 .

[3] H. Bateman,et al. Halley's Methods for Solving Equations , 1938 .

[4] Florian A. Potra,et al. On enclosing simple roots of nonlinear equations , 1993 .

[5] A. Ostrowski. Solution of equations in Euclidean and Banach spaces , 1973 .

[6] Muhammad Aslam Noor,et al. A new modified Halley method without second derivatives for nonlinear equation , 2007, Appl. Math. Comput..

[7] F. Potra. On an iterative algorithm of order 1.839… for solving nonlinear operator equations ∗) , 1985 .

[8] Alfredo Germani,et al. Higher-Order Method for the Solution of a Nonlinear Scalar Equation , 2006 .

[9] M. Frontini,et al. Some variant of Newton's method with third-order convergence , 2003, Appl. Math. Comput..

[10] Changbum Chun,et al. Certain improvements of Chebyshev-Halley methods with accelerated fourth-order convergence , 2007, Appl. Math. Comput..

[11] Changbum Chun,et al. Iterative methods improving newton's method by the decomposition method , 2005 .

[12] Florian A. Potra,et al. On Two Higher Order Enclosing Methods of J. W. Schmidt , 1988 .