Variational Iteration Method for a Nonlinear Equation with Multiple Roots

• 作 者: LIULandong;SUXinwei;
• 机 构: School of Science,China University of Mining and Technology,Beijing 100083
• 出 处: 中央高校基本科研业务费项目研究成果学术交流会
• 发表日期: 2011年期

　　In this paper, we are concerned with finding multiple zeros of the nonlinear equation f(x) =0 while the multiplicity is unknown explicitly.We present a new family of iterative methods which is obtained by means of Ji-huan Hes variational iteration method.The new methods are generalization of the modified Newton method.We prove that it is quadratical convergent and further we choose the appropriate value of parameter α such that the methods convergence can reach third-order.The advantage of new methods is not necessary to know the multiplicity of root in advance but we still compute the approximate root xn with high-efficiency.Finally, some numerical examples are given to show the performance of the presented methods compared with some known third-order methods.