An Iterative Method with Fifteenth-Order Convergence to Solve Systems of Nonlinear Equations

被引：0
作者：
Srivastava A. [1 ]
机构：
[1] Department of Mathematics, Indian Institute of Technology Gandhinagar VGEC Complex, Ahmedabad, 382424, Chandkheda
来源：
Computational Mathematics and Modeling | 2016年 / 27卷 / 4期
关键词：
efficiency index; finite element method; Newton’s method; nonlinear elliptic partial differential equations; Nonlinear equations; order of convergence;
D O I：
10.1007/s10598-016-9339-9
中图分类号：
学科分类号：
摘要：
In this article, a modification of Newton’s method with fifteenth-order convergence is presented. The modification of Newton’s method is based on the method of fifth-order convergence of Hu et al. First, we present theoretical preliminaries of the method. Second, we solve some nonlinear equations and then systems of nonlinear equations obtained by means of the finite element method. In contrast to the eleventh-order M. Raza method, the fifteenth-order method needs less function of evaluation per iteration, but the order of convergence increases by four units. Numerical examples are given to show the efficiency of the proposed method. © 2016, Springer Science+Business Media New York.
引用
收藏
页码：497 / 510
页数：13
相关论文
共 17 条
  • [1] Atluri S.N., Methods of Computer Modeling in Engineering and Sciences, Tec. Sci, Press, (2002)
  • [2] Atluri S.N., Liu H.T., Han Z.D., Meshless local Petrov–Galerkin (MLPG) mixed collocation method for elasticity problems, Comput. Model. Eng. Sci., 14, pp. 141-152, (2006)
  • [3] Atluri S.N., Shen S., The meshless local Petrov–Galerkin (MLPG) method: a simple and less-costly alternative to the finite and boundary element methods, Comput. Model. Eng. Sci., 3, pp. 11-51, (2002)
  • [4] Kumar M., Singh A.K., Srivastava A., Various Newton-type iterative methods for solving nonlinear equations, J. Egypt. Math. Soc., 21, pp. 334-339, (2013)
  • [5] Li X., Wu Z., Wang L., Zhang Q., A ninth-order Newton-type method to solve systems of nonlinear equations, J. Res. Rev. App. Sci., 16, pp. 224-228, (2013)
  • [6] Raza M., Eleventh-order convergent iterative method for solving nonlinear equations, Int. J. Appl. Math., 25, pp. 365-371, (2012)
  • [7] Hu Z., Guocai L., Tian L., An iterative method with ninth-order convergence for solving nonlinear equations, Int J. Contemp. Math. Sci., 6, pp. 17-23, (2011)
  • [8] Noor M.A., Khan W.A., Noor K.I., Al-Said E., Higher-order iterative methods free from second derivative for solving nonlinear equations, Int. J. Phys. Sci., 6, pp. 1887-1893, (2011)
  • [9] Al-Subaihi I.A., Shatnawi M.T., Siyyam H.I., A ninth-order iterative method free from second derivative for solving nonlinear equations, Int. J. Math. Anal., 5, pp. 2337-2347, (2011)
  • [10] Alberty J., Carstensen C., Funken S.A., Remarks around 50 lines of Matlab: short finite element implementation, Numer. Algorithms, 20, pp. 117-137, (1999)
12