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...

We show that the spectrum of linear delay differential equations with large delay splits into two different parts. One part, called the strong spectrum, converges to isolated points when the delay parameter tends to infinity. The other part, called the pseudocontinuous spectrum, accumulates near criticality and converges after rescaling to a set of spectral curves, called the asymptotic continu...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

This paper summarizes recent research on an approach for the analytical solution to systems of delay differential equations developed using the Lambert W function [26, 29], and its applications [25, 28]. Also, several outstanding research problems associated with the solution of systems of delay differential equations using the matrix Lambert W function are highlighted. The solution has the for...