Abstract

Newton's method (quadratic convergence) is usually the most used iterative method for solving nonlinear systems of equations. In this paper, we construct, from the modification of a third-order iterative method of Chebyshev-type, a new family of fourthorder iterative methods which is more efficient than Newton's method. We study the efficiency of the methods from the efficiency index and the computational efficiency. We also analyse the semilocal convergence of the methods and apply all the analysis to the solution of mildly nonlinear elliptic boundary value problems. © 2010 Civil-Comp Press.

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