A Natural Homotopy Analysis Method for Nonlinear Delay Differential Equations

Homotopy analysis method and its application for singularly perturbed delay differential equations with layer behavior

در این مقاله یک روش تحلیلی بر پایه‌ی روش تحلیل هموتوپی برای حل معادله دیفرانسیل-تفاضلی اختشاشی منفرد ارائه شده است. معادلات مورد بررسی در این مقاله از نوع تاخیری است که دارای رفتار لایه مرزی نیز هستند. تفاوت روش تحلیل هموتوپی با روشهای تحلیلی دیگر فراهم کردن یک راه ساده برای کنترل ناحیه همگرایی سری جواب بدست آمده معادله با استفاده از پارامتر کمکی تعبیه شده در این روش است. در این مقاله صحت و درس...

Homotopy Analysis Sumudu Transform Method for Nonlinear Equations

Homotopy Analysis Method for Delay-integro-differential Equations

In this paper, we implement the homotopy analysis method to solve delay-integro-differential equations. The convergence of the method is investigated. In the end, numerical experiments are presented to illustrate the computational effectiveness of the method.

Homotopy Analysis Method for Nonlinear Differential Equations with Fractional Orders

Most problems in science and engineering are nonlinear. Thus, it is important to develop efficient methods to solve them. In the past decades, with the fast development of high-quality symbolic computing software, such as Maple, Mathematica and Matlab, analytic as well as numerical techniques for nonlinear differential equations have been developed quickly. The homotopy analysis method (HAM) [1...

Modified homotopy perturbation method for stiff delay differential equations (DDEs)

In this paper, an efficient modification is introduced into the well-known homotopy perturbation method which proves very effective to control the convergence region of approximate solution. By using this scheme, explicit exact solution is calculated in the form of a convergent power series with easily computable components. The proposed algorithm is tested on some neutral stiff functional-diff...