An Explicit Numerical Technique for Nonlinear Nonlocal Time-Delay Dynamical Systems via Quadratic Spline Approach

محورهای موضوعی : مجله بین المللی ریاضیات صنعتی

H. Panj-mini ¹ , B. Parsa Moghaddam ² , E. Hashemizadeh ³

1 - Department of Mathematics, Lahijan Branch, Islamic Azad university, Lahijanو Iran.
2 - Department of Mathematics, Lahijan Branch, Islamic Azad University, Lahijan, Iran.
3 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran.

تاریخ دریافت : 1400/03/08 تاریخ پذیرش : 1400/07/10 تاریخ انتشار : 1400/10/11

کلید واژه: quadratic spline interpolation, Chaotic attractor, Fractional delay differential equation, Fractional calculus, numerical method, Ikeda model, Hutchinson model,

چکیده مقاله :

Dynamical systems with delay are widespread in nature. The study of time-delay induced changes in the collective behavior of systems of coupled nonlinear oscillators is a subject of great interest, both because of its fundamental importance from the point of view of dynamical systems and because of its practical applications. In this paper, an explicit technique is proposed for numerical solution of nonlocal dynamical systems with time delay. The proposed method is adopted quadratic spline interpolation. Then, the error analysis of the developed method is discussed. It is exploited in the discussion of nonlocal delay Ikeda and Hutchinson models. Finally, the performance of the presented approach is verified by applying the error and convergence study for different values of fractional order parameters.

چکیده انگلیسی:

در این مقاله، روشی صریح برای حل عددی معادلات دیفرانسیل غیرموضعی با تأخیر در زمان ارائه و مورد بررسی قرار می گیرد. در روش ارائه شده، درونیابی اسپلاین مربعی بکار گرفته شده است و خطای روش ارائه شده آنالیز گردیده است. کارایی و اعتبار روش پیشنهادی در مدل‌های آیکدا و هاتچینسون غیرموضعی تأخیری با استناد مفاهیم خطا و همگرایی روشهای عددی به ازای مقادیر مختلف پارامترهای مرتبه کسری نمایان شده است.

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