A novel approach in applying homotopy analysis method

Subject Areas : Numeric Analyze

Mojtaba  Ghanbari ¹ (Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran.)

Received: 2021-06-14 Accepted : 2022-10-23 Published : 2023-09-01

Keywords: روش تحلیل هموتوپی, سری جواب, جواب تقریبی, مسائل مقدار اولیه ی غیرخطی,

Abstract :

One of the most important methods for solving linear and nonlinear problems is the homotopic analysis method, which was proposed by Liao in 1992. The main purpose of this paper is to present a modification of homotopy analysis method (HAM), which is called successive homotopy analysis method (SHAM). Several numerical examples are presented to present a comparison between the results obtained by homotopy analysis method and its successive type. The results show that the calculation volume in the successive homotopy analysis method is less that the homotopy analysis method. Also, unlike the homotopy analysis method, the numerical solutions obtained by the successive homotopy analysis method are satisfactory over a relatively wide range. So, by using the successive homotopy analysis method, various types of linear and nonlinear mathematical equations and also some nonlinear equations which are obtained in other scientific branches, for instance physics, mechanics and etc, can be solved numerically.

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