Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations
نویسندگان
چکیده
منابع مشابه
Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations
We study the singularly perturbed state-dependent delay-differential equation εẋ(t) = −x(t)− kx(t− r), r = r(x(t)) = 1 + x(t), (∗) which is representative of a broader class of such equations of the form εẋ(t) = g(x(t), x(t− r)), r = r(x(t)). It is known that for every sufficiently small ε > 0, equation (∗) possesses at least one so-called slowly oscillating periodic solution, and moreover, the...
متن کاملHomotopy 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...
متن کاملA 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...
متن کاملAn 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2011
ISSN: 0022-0396
DOI: 10.1016/j.jde.2010.10.024