An improvement to double-step Newton method and its multi-step version for solving system of nonlinear equations and its applications

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• 作者：Kalyanasundaram Madhu ; D. K. R. Babajee ; Jayakumar Jayaraman
• 关键词：System of nonlinear equation ; Newton’s method ; Order of convergence ; Multi ; step method ; Fréchet derivatives
• 刊名：Numerical Algorithms
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：74
• 期：2
• 页码：593-607
• 全文大小：
• 刊物类别：Computer Science
• 刊物主题：Numeric Computing; Algorithms; Algebra; Theory of Computation; Numerical Analysis;
• 出版者：Springer US
• ISSN：1572-9265
• 卷排序：74

文摘

In this work, we have improved the order of the double-step Newton method from four to five using the same number of evaluation of two functions and two first order Fréchet derivatives for each iteration. The multi-step version requires one more function evaluation for each step. The multi-step version converges with order 3r+5, r≥1. Numerical experiments are done comparing the new methods with some existing methods. Our methods are also tested on Chandrasekhar’s problem and the 2-D Bratu problem to illustrate the applications.