A fourth order regula-falsi Newton-like method for enclosing simple zeros of nonlinear equations. (2016) - Nisha, Shwet; Parida, Pradip K.
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.