Ferdowsi University of Mashhad Iranian Journal of Numerical Analysis and Optimization 2423-6977 11 1 2021 03 01 A high-order algorithm for solving nonlinear algebraic equations 107 115 39537 10.22067/ijnao.2021.11329.0 EN A. Ghorbani Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. 0000-0002-5561-7425 M. Gachpazan Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. 0000-0001-5662-0207 Journal Article 2020 08 28 A fourth-order and rapid numerical algorithm, utilizing a procedure as Runge–Kutta methods, is derived for solving nonlinear equations. The method proposed in this article has the advantage that it, requiring no calculation of higher derivatives, is faster than the other methods with the same order of convergence. The numerical results obtained using the developed approach are compared to those obtained using some existing iterative methods, and they demonstrate the efficiency of the present approach. order of convergence Newton–Raphson method Householder iteration method Nonlinear equations https://ijnao.um.ac.ir/article_39537_2d686296ea060d41b2c67502ec3c1f39.pdf