An improved regula-falsi method for enclosing simple zeros of nonlinear equations

In this paper, an improved regula-falsi method of order three for finding zeros of nonlinear equations f(x) = 0. where f : [a, b] subset of R -> R is a continuously differentiable function. is proposed. The proposed method consists of a combination of usual regula-falsi method and a Newton-like method to solve f(x) = 0. It starts with a suitably chosen x(0) (generally near to the zero r) and generates a sequence of successive iterates x(n), n = 0. 1.... which converges cubically to the zero r. If for an interval [a,b]. the diameter of [a,b] be defined as (b - a). then the proposed method generates a sequence of diameters {(b(n) - a(n))} for the sequence of intervals {(a(n), b(n))} each enclosing the zero r and converges cubically to 0. The method is tested on a number of numerical examples and results obtained show that the proposed method is very effective when compared Nvith some existing methods used to solve same problems. (c) 2005 Elsevier Inc. All rights reserved.