A fourth order regula-falsi Newton-like method for enclosing simple zeros of nonlinear equations

Abstract

In this paper, we have developed an improved regula falsi method of order four for finding simple roots of nonlinear equations f(x) = 0, where f : [a; b] ⊂ R → R is a given continuously differentiable function. This is done by combining a Newton-like method of order four to solve f(x) = 0 and the usual regula-falsi method. Convergence analysis for the method has been given in this paper. Finally some numerical examples are presented and comparison has been made with existing results.