IJPAM: Volume 57, No. 4 (2009)

SOME THREE-STEP ITERATIVE METHODS FREE FROM
SECOND ORDER DERIVATIVE FOR FINDING SOLUTIONS
OF SYSTEMS OF NONLINEAR EQUATIONS

M.T. Darvishi
Department of Mathematics
Faculty of Science
Razi University
Kermanshah, 67149, IRAN
e-mail: darvishimt@yahoo.com


Abstract.We present some three-step iterative methods to find roots of several variables functions. These methods do not need the evaluation of the second order derivative of the given $n$-valued nonlinear function. The new methods are extensions of iterative methods to find roots of nonlinear equation $f(x)=0$. Convergency of the methods is proved. We provide numerical results to show the efficiency of the new methods for systems of nonlinear equations. It is observed that new methods take less number of iterations than the Newton's method. We compare the run time of the Newton's method and new three-step algorithms. Residual falls of logarithm of residuals show a high-order convergence of the new methods. Also we apply the new algorithms to solve the Chandrasekhar integral equation in radiative transfer.

Received: November 20, 2009

AMS Subject Classification: 65H10, 65B99

Key Words and Phrases: three step method, root finding, iteration number, nonlinear system, CPU-time, convergency

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 57
Issue: 4