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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، بهار و تابستان 2021، صفحه 107-115 اصل مقاله (1.49 MB) | ||
| 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 | ||
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1. Babolian, E. and Biazar, J. Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Comput. 132 (2002), 167–172. 2. Basto, M., Semiao, V. and Calheiros, F.L. A new iterative method to compute nonlinear equations, Appl. Math. Comput. 173 (2006), 468–483. 3. Chun, C. Iterative methods improving Newton’s method by the decompo sition method, Comput. Math. Appl. 50 (2005), 1559–1568. 4. Golbabai, A. and Javidi, M. A new family of iterative methods for solving system of nonlinear algebraic equations, Appl. Math. Comput. 190 (2007), 1717–1722. 5. He, J.H. A new iterative method for solving algebraic equations, Appl. Math. Comput. 135 (2003), 81–84. 6. Householder, A.S. The numerical treatment of a single nonlinear equation, McGraw-Hill, New York, 1970. 7. Maheshwari, A.K. A fourth-order iterative method for solving nonlinear equations, Appl. Math. Comput. 211 (2009), 383–391. 8. Noor, M.A. New iterative schemes for nonlinear equations, Appl. Math. Comput. 187 (2007), 937–943. | ||
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