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

摘要

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 {(bn−an)} and the iterative sequence {(xn−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.