SOME MULTI-STEP ITERATIVE SCHEMES FOR SOLVING NONLINEAR EQUATIONS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
In this paper, we suggest and analyze a family of multi-step iterative methods which do not involve the high-order differentials of the function for solving nonlinear equations using a different type of decomposition (mainly due to Noor and Noor [15]). We also discuss the convergence of the new proposed methods. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative method. Our results can be considered as an improvement and refinement of the previous results.
Abstract
In this paper, we suggest and analyze a family of multi-step iterative methods which do not involve the high-order differentials of the function for solving nonlinear equations using a different type of decomposition (mainly due to Noor and Noor [15]). We also discuss the convergence of the new proposed methods. Several numerical examples are given to illustrate the efficiency and the performance of the new iterative method. Our results can be considered as an improvement and refinement of the previous results.
참고문헌 (16)
- S. Abbasbandy, "Improving Newton Raphson method for nonlinear equations by modi- fied Adomian decomposition method", Appl. Math. Comput, 145, pp.887~893 (2003)
- G. Adomian, "Nonlinear Stochastic Systems and Applications to Physics" (1989), Kluwer Aca- demic Publishers
- G. Adomian, "A review of the decomposition method and some recent results for nonlinear equations", Math. Comput. Model, 13(7), pp.17~43 (1992)
- G. Adomian, "Solving Frontier Problems of Physics: The Decomposition Method" (1994), Kluwer
- G. Adomian, "Noise terms in decomposition series solution Comput", Math. Appl, 24(11), pp.61~64 (1992)
- C. Chun, "Iterative methods improving Newton method by the decomposition method", Comput. Math. Appl, 50, pp.1559~1568 (2005)
- V. Daftardar-Geiji, "An iterative method for solving nonlinear functional equations", J. Math. Anal. Appl, 316, pp.753~763 (2006)
- M. Frontini, "Some variants of Newton method with third order conver- gence", J. Comput. Appl. Math, 140, pp.419~426 (2003)
- J.H. He, "A new iteration method for solving algebraic equations", Appl. Math. Comput, 135, pp.81~84 (2003)
- H.H. Homeier, "On Newton-type methods with cubic convergence", J. Comput. Appl. Math, 176, pp.425~432 (2005)
- X. Lao, "A note on the new iteration for solving algebraic equations", Appl. Math. Com- put, 171, pp.1177~1183 (2005)
- M.A. Noor, "Numerical Analysis and Optimization, Lecture Notes" (2006), COMSATS Institute of Information Technology
- M.A. Noor, "New family of iterative methods for nonlinear equations", Appl. Math. Comput, 190, pp.553~558 (2007)
- M.A. Noor, "Three-step iterative methods for nonlinear equations", Appl. Math. Comput, 183, pp.322~327 (2006)
- M.A. Noor, "Some iterative schemes for nonlinear equations", Appl. Math. Comput, 183, pp.774~779 (2006)
- S. Weerakoon, "A variant of Newton method with accelerated third order convergence", Appl. Math. Lett, 17, pp.87~93 (2000)