A new approach for solving nonlinear system of equations using Newton method and HAM

Iranian Journal of Numerical Analysis and Optimization

مقاله 3، دوره 4، شماره 2 - شماره پیاپی 6، بهمن 2014، صفحه 57-72   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v4i2.32555

نویسندگان

J. Izadian^{* 1}؛ R. Abrishami¹؛ M. Jalili²

¹Department of Mathematics, Faculty of Sciences, Mashhad Branch, Islamic Azad University, Mashhad, Iran.

²Department of Mathematics, Neyshabur Branch, Islamic Azad University, Neyshabur, Iran.

چکیده

A new approach utilizing Newton Method and Homotopy Analysis Method (HAM) is proposed for solving nonlinear system of equations. Accelerating the rate of convergence of HAM, and obtaining a global quadratic rate of convergence are the main purposes of this approach. The numerical results demonstrate the efficiency and the performance of proposed approach. The comparison with conventional homotopy method, Newton Method and HAM shows the great freedom of selecting the initial guess, in this approach.

کلیدواژه‌ها

Homotopy Analysis Method؛ Zero order deformation equations؛ control convergence parameter؛ Newton's method؛ Iterative method؛ multi-step iterative method؛ order of convergence

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