Homotopy analysis method and its application for singularly perturbed delay differential equations with layer behavior
Authors
Abstract:
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 درستی و همچنین دقت بالای جوابهای حاصل از حل معادله دیفرانسیل-تفاضلی اختشاشی منفرد تاخیری با استفاده از روش تحلیل هموتوپی با آوردن دو مثال عددی نشان داده شده است، با مقایسه جوابهای به دست آمده از روش تحلیل هموتوپی با روشهای عددی دیگر متوجه می‌شویم که استفاده از روش تحلیل هموتوپی برای حل معادله مذکور علاوه بر راحتی در پیاده سازی آن روی این نوع مسائل، نتایج بهتری را نیز فراهم می‌آورد. بعلاوه قضایای همگرایی روش مورد بحث و بررسی قرار گرفته است.
similar resources
Numerical algorithm for singularly perturbed delay differential equations with layer and oscillatory behavior
We consider the numerical approximation of singularly perturbed linear second order reaction-diffusion boundary value problems with a small shift(δ) in the undifferentiated term and the shift depends on the small parameter(ǫ). The presence of small parameter induces twin boundary layers. The problem is discretized using standard finite difference scheme on an uniform mesh and the retarded argum...
full textA Parameter Robust Method for Singularly Perturbed Delay Differential Equations
Uniform finite difference methods are constructed via nonstandard finite difference methods for the numerical solution of singularly perturbed quasilinear initial value problem for delay differential equations. A numerical method is constructed for this problem which involves the appropriate Bakhvalov meshes on each time subinterval. The method is shown to be uniformly convergent with respect t...
full textAn Exponentially Fitted Method for Singularly Perturbed Delay Differential Equations
This paper deals with singularly perturbed initial value problem for linear first-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first-order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation paramet...
full textNumerical Integration Method for Singularly Perturbed Delay Differential Equations
In this paper, we present a numerical integration method to solve singularly perturbed delay differential equations. In this method, we first convert the second order singularly perturbed delay differential equation to first order neutral type delay differential equation and employ the numerical integration. Then, linear interpolation is used to get three term recurrence relation which is solve...
full textBoundary layer analysis for nonlinear singularly perturbed differential equations
This paper focuses on the boundary layer phenomenon arising in the study of singularly perturbed differential equations. Our tools include the method of lower and upper solutions combined with analysis of the integral equation associated with the class of nonlinear equations under consideration. Key words and phrases: singularly perturbed systems, three–point boundary value problem, method of l...
full textA method based on the meshless approach for singularly perturbed differential-difference equations with Boundary layers
In this paper, an effective procedure based on coordinate stretching and radial basis functions (RBFs) collocation method is applied to solve singularly perturbed differential-difference equations with layer behavior. It is well known that if the boundary layer is very small, for good resolution of the numerical solution at least one of the collocation points must lie in the boundary layer. In ...
full textMy Resources
Journal title
volume 6 issue 23
pages 29- 38
publication date 2020-04-01
By following a journal you will be notified via email when a new issue of this journal is published.
Hosted on Doprax cloud platform doprax.com
copyright © 2015-2023