A Novel Geometric Modification To The Regula Falsi Method To Achieve Cubic Convergence Order

Abstract

Chen and Li (2007) presented a family of quadratically convergent Regula Falsi iterative methods for solving nonlinear equations f(x) =0. Additionally, it is demonstrated there that the iterative point sequence converges to zero. This work aims to accelerate the method convergence from quadratic to cubic forms. This can be achieved by substituting an appropriately specified function, p(x), for the parameter p in Chen and Li's iteration. A convergence theorem is used to determine the cubic convergence of the iterate sequence to the root. The numerical examples show that the proposed method is more efficient and required fewer number of iterations in comparison to Newton's method, Steffensen's method, Regula Falsi method, and those provided in Chen and Li.