تحلیل همگرایی روش شبه‌طیفی ژاکوبی برای معادلات انتگرال - دیفرانسیل کسری تأخیری در فضای $L^2_{\omega^{\alpha ,\beta}}(I)$

پیک رایگان, نرگس; قوتمند, مهدی; نوری اسکندری, محمد هادی

doi:10.22055/jamm.2023.39637.1995

تحلیل همگرایی روش شبه‌طیفی ژاکوبی برای معادلات انتگرال - دیفرانسیل کسری تأخیری در فضای $L^2_{\omega^{\alpha ,\beta}}(I)$

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده علوم ریاضی، دانشگاه صنعتی شاهرود، شاهرود، ایران

10.22055/jamm.2023.39637.1995

چکیده

روش های شبه طیفی در سال های اخیر به دلیل دقت و سرعت همگرایی بالایی که دارند

برای حل بسیاری از رده های معادلات دیفرانسیل و انتگرال به کار گرفته شده اند. در این مقاله، یک

روش شبه طیفی ژاکوبی کارا برای حل رده ای از معادلات انتگرال - دیفرانسیل کسری تأخیری ارائه

می کنیم. سپس با ارائه چندین لم و قضیه، همگرایی روش را روی فضای

$L^2_{\omega^{\alpha ,\beta}}(I)$

بررسی کرده و کران های خطا را مشخص می کنیم.

کلیدواژه‌ها

موضوعات

معادلات دیفرانسیل

عنوان مقاله [English]

Convergence analysis of Jacobi pseudospectral method for delay fractional integral-differential equations in $L^2_{\omega^{\alpha ,\beta}}(I)$ space

نویسندگان [English]

Narges Peykrayegan
Mehdi Ghovatmand
Mohammad Hadi Noori Skandari

Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran

چکیده [English]

In recent years, pseudospectral methods have been used for solving many classes of differential and integral equations due to their high accuracy and rate of convergence. In this paper, we present an efficient Jacobi pseudospectral method for solving a class of fractional delay integral-differential equations. Then, by presenting several lemmas and theorems, we investigate the convergence of the method on space

$ L ^ 2 _ {\ omega {alpha \ alpha, \ beta}} (I) $ and identify the error boundaries.

کلیدواژه‌ها [English]

Riemann-Liouville and Caputo fractional derivatives
Lagrange interpolation polynomials
Jacobi-Gauss points
Fractional delay integral-differential equations

مراجع

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