An improved regula falsi method with quadratic convergence of both diameter and point for enclosing simple zeros of nonlinear equations

A new method of regula falsi type with global convergence for finding a simple root x* of a nonlinear equation f (x) = 0 in the interval [a, b] is presented in this paper. The new method is shown to be quadratically convergent. Both the sequences of diameters {(b(n) - a(n))} and the iterative sequence {(x(n) - x*)} are quadratically convergent to zero. The new method has been tested on a series of published examples. The numerical results show that the new method is very effective. (C) 2002 Published by Elsevier Inc.