Archive
Special Issues Volume 3, Issue 4, August 2014, Page: 130-136
Generalized Difference Formula for a Nonlinear Equation
Hamideh Eskandari, Department of Mathematics, Payame Noor University, I. R. Iran
Received: Jul. 12, 2014;       Accepted: Jul. 22, 2014;       Published: Jul. 30, 2014
Abstract
In this paper, a new iteration scheme is proposed to solve the roots of a nonlinear equation. It is the purpose of this paper to show that, although the new iteration method seems to be of high convergence, the results are promising in that it requires more computation work and even be divergent. In here, we use iteration method that applied derivatives of the first order and the second order; we substitute difference formulas in iteration formulas. This method cause that our iteration method have not any derivative formulas.
Keywords
Newton Method, Hybrid Method, Halley Iteration, Steffenson Method
Hamideh Eskandari, Generalized Difference Formula for a Nonlinear Equation, Applied and Computational Mathematics. Vol. 3, No. 4, 2014, pp. 130-136. doi: 10.11648/j.acm.20140304.14
Reference

Atkinson, Kendall E. An introduction to numerical analysis, John Wiley & Sons, (1988).

Stoer .J, Bulirsch .R, Introduction to numerical analysis, Springer-Verlag, (1983).

Hildebrand .F.B, Introduction to numerical analysis, Tata McGraw-Hill, (1974).

Nasr-Al-Din, Ide. A new hybrid iteration method for solving algebraic equations, Applied Mathematics and Computation, 195 (2008) 772-774.

Fang .T, Fang .G, Lee .C.F, A new iteration method with cubic convergence to solve nonlinear algebraic equations, Applied Mathematics and Computation, 175 (2006) 1147-1155.

Eskandari .Hamideh, a new numerical solving method for equations of one variable, International Journal of Applied Mathematics and Computer Sciences, 5:3(2009) 183-186.

Cheney .E .W, Kincaid .D, Numerical mathematics and computing, Thomson Learning, 2003.

Stewart .G .W, after notes on numerical analysis, SIAM, 1996.

Pav .Steven E. Numerical Methods Course Notes, 2005.

Quarteroni .A, Sacco .R, Saleri .F, Numerical Mathematics, Springer, 2000. 