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A High-Order Derivative Free Iteration Method for Solving Nonlinear Equations

Author: ChuXuLei
Tutor: ZhangGuoFeng
School: Lanzhou University
Course: Computational Mathematics
Keywords: Newton's method Iterative formula Nonlinear equations No derivative Order of convergence
CLC: O241.7
Type: Master's thesis
Year: 2011
Downloads: 56
Quote: 0
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Abstract


In this paper, the higher-order iterative methods for solving nonlinear equations without derivation . Already some iterative methods for solving nonlinear equations , such as Newton iterative method , as well as some high-end three-step iteration of iterative method , the first derivative exists and ranging zero . In practical applications , many situations are derivative unavailable , the other to calculate the derivative of the function will be to increase the computational complexity , in order to solve this problem, the paper based R.Thukrαl and MSPetkovic [ 45] proposed an 8 - order iteration the method , using central difference quotient approximation instead of the first derivative of the function , to construct a order iterative method for solving nonlinear equations without the derivative of . Prove the convergence of the iterative algorithm and convergence order . Calculation of some numerical examples to verify the correctness of the method ; and compared with existing methods , and verify the effectiveness of the algorithm .

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CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > Nonlinear algebraic equations and numerical solution of the transcendental equation
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