International Journal of Mathematics and Computational Science
Articles Information
International Journal of Mathematics and Computational Science, Vol.2, No.3, Jun. 2016, Pub. Date: Aug. 25, 2016
The Approximate Calculation of the Roots of Algebraic Equation Through Monte Carlo Method
Pages: 64-68 Views: 1348 Downloads: 851
[01] Vahid Mirzaei Mahmoud Abadi, Faculty of Physics, Shahid Bahonar University of Kerman, Kerman, Iran.
[02] Shila Banari Bahnamriri, Tabari Institute of Higher Education of Babol, Babol, Iran.
Finding the root of nonlinear algebraic equations is an issue usually found in engineering and sciences. This article presents a new method for the approximate calculation of the roots of a one-variable function through Monte Carlo Method. This method is actually based on the production of a random number in the target range of the root. Finally, some examples with acceptable error are provided to prove the efficiency of this method.
Monte Carlo, Root Finding, Nonlinear Algebraic Equation
[01] L. Petkovic et al., On the conctruction of simultaneous method for multiple zeros, Non-Linear Anal., Theory, Meth. Appl. 30(1997) 669-676.
[02] J. H. He, Newton-like iteration method for solving algebraic equations, Commun. Nonl-Iinear Sci. Numer. Simulation 3(2) (1998).
[03] J. H. He, Improvement of Newton-like iteration method, Int. J. Nonlinear Sci. Numer. Simulation 1(2) (2000) 239-240.
[04] T. Yamamoto, Historical development in convergence analysis for Newtons and Newt on-loke method, J Comput, Appl, Math,. 124 (2000) 1-23.
[05] Adomian G, Rach R., On the solution of algebraic equations by the decomposition method, Math. Anal. Appl., 105, (1985), 141-166.
[06] S. Abbasbandy, M. T. Darvishi, A numerical solution of Burgers equation by modified Adomian method, Appl. Math. Comput., 163 (2005), 1265-1272.
[07] K. Abbaoui, Y. Cherruault, Convergence of Adomian’s Method Applied to Nonlinear Equations, Math. Comput. Model., 20(9), (1994), 69-73.
[08] E. Babolian, J. Biazar, Solution of nonlinear equations by modified Adomian decomposition method, Appl. Math. Computation, 132 (2002) 167-172.
[09] E. Babolian, J. Biazar, On the order of convergence of Adomian method, Applied Mat- hematics and Computation, 130, (2002), 383-387.
[10] E. Babolian, A. Davari, Numerical implementation of Adomian decomposition method, Appl. Math. Comput., 153, (2004), 301-305.
[11] Y. Cherruault, Convergence of Adomian’s Method, Kybernetes, 8(2), 1998, 423-426.
[12] Cherruault Y, Adomian G., Decomposition methods: a new proof of convergence. Math. Comput. Modell., 18, (1993), 103-106.
[13] J. H. He, Homotpy perturbation method, Comp. Math. Appl. Mech. Eng. 178 (1999) 257–262.
[14] J.-H. He, A coupling method of homotopy technique and perturbation technique for Nonlinear problems, Intm J Nonlinear Mech. 35(1) (2000) 37-43.
[15] S. Abbasbandy, Modified homotopy perturbation method for nonlinear equation and Comparison with Adomian decomposition method, Applied Mathemetics and comput172 (2006) 431-438.
[16] Richard Belman, Perturbation Techniques in Mathematics, Physics, and Engineering. Dover Pub. Inc., New York, 1972.
[17] Brown. J. W, Churchill. R. V, Coplex Variables and Applications, Sixth Editoin, McGraw-Hill, 1996.
[18] T. Yamamoto, Historical development in convergence analysis for Newton’s and Newton-likemethods, J. Comput. Appl. Math. 124 (2000) 1–23.
[19] Ji. Huan He, Anew iteration method for solving algebraic equations, Appl. Math. 135 (2003) 81-84.
[20] S. Abbasbandy, Improving Newton-Raphson method for nonlinear equations by mod- Ified Adomian decomposition method, Appl. Math. 145 (2003) 887-893.
[21] Changbum chun, Anew iterative method for solving nonlinear equations, Appl. Math, 178 (2006) 415-422.
[22] S. Abbsbandy, Y. Tan, S. J Liao, Newton-Homotopy analysis method for nonlinear eq-Uations, Applied Mathemetics and comput. 188 (2007) 1794=1800.
[23] E. Babolian, T. Lotfi, F. M. Yaghoobi, Solving no linear equation by perturbation technique and Lagrange expansion, extended abstract of the 18th seminar on mathematical analysis and it application, 2009, pp 154-157.
[24] Krandick, W., Mehlhorn, K. "New Bounds for the Descartes Method"; Journal of Symbolic Computation, 41, (2006), 49-66.
[25] Sharma, V. "Complexity Analysis of Algorithms in Algebraic Computation"; Ph.D. Thesis, Department of Computer Sciences, Courant Institute of Mathematical Sciences, New York University, 2007.
[26] Cordero A, Torregrosa JR (2006) Variants of Newton’s method for functions of several variables. Appl Math Comput 183:199–208.
[27] Cordero A, Hueso JL, Martínez E, Torregrosa JR (2012) Increasing the convergence order of an iterative method for nonlinear systems. Appl Math Lett 25:2369–2374.
[28] Grau-Sánchez M, Noguera M (2012) A technique to choose the most efficient method between secant method and some variants. Appl Math Comput 218:6415–6426.
[29] Petkovi ́ MS, Neta B, Petkovi ́ LD, Džuni ́ J (2013) Multipoint methods for solving nonlinear equations. Elsevier, Boston.
[30] Sharma JR, Arora H (2014) Efficient Jarratt-like methods for solving systems of nonlinear equations. Calcolo 51:193–210. doi: 10.1007/s10092-013-0097-1.
[31] Sharma JR, Guha RK, Sharma R (2013) An efficient fourth order weighted-Newton method for systems of nonlinear equations. Numer Algorithms 62:307–323.
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