A high-order algorithm for solving nonlinear algebraic equations

Iranian Journal of Numerical Analysis and Optimization

مقاله 6، دوره 11، شماره 1 - شماره پیاپی 19، خرداد 2021، صفحه 107-115   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.2021.11329.0

نویسندگان

A. Ghorbani^* ؛ M. Gachpazan

Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

چکیده

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.

کلیدواژه‌ها

Order of convergence؛ Newton–Raphson method؛ Householder iteration method؛ Nonlinear equations

مراجع