# بررسی عددی و تخمین خطا برای معادلات انتشار کسری-زمانی چندگانه‌ی مبتنی بر عملگر کسری جدید

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه ریاضی کاربردی، دانشکده علوم ریاضی، دانشگاه شهرکرد، شهرکرد، ایران

2 گروه ریاضی دانشگاه پیام نور، صندوق پستی 4697-19395، تهران ایران

چکیده

در این مقاله، روشی عددی برای حل معادلات انتشار کسری-زمانی چندجمله‌‌ای مرتبط با یک عملگر کسری جدید ارائه شده است. بر اساس روش تفاضل متناهی، یک طرح نیمه-گسسته در مسیر زمان به‌دست آورده شده و سپس برای گسسته سازی مکانی روش تقریب طیفی چبیشف استفاده شده است. همچنین آنالیز پایداری و خطای روش طیفی پیشنهادی بررسی شده است. بیشتر، توسعه‌‌ی معادله‌ی انتشار کسری چندجمله‌‌ای به معادله‌ی مرتبه‌ی توزیعی در نظر گرفته شده و روی آن تجزیه و تحلیل عددی صورت گرفته شده است. در پایان، با استفاده از برخی مثال‌های عددی‌، نتایج تئوری مورد تایید واقع شده است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

### Numerical investigation and error estimate for multi-term time-fractional diffusion equations based on new fractional operator

نویسندگان [English]

• Mojtaba Fardi 1
• ٍٍEbrahim Amini 2
1 Department of Applied Mathematics, Faculty of Mathematical Science, Shahrekord University, Shahrekord, P. O. Box 115, Iran.
2 Department of Mathematics, Payme Noor University, P. O. Box 19395-4697 Tehran, Iran.
چکیده [English]

In this paper‎, ‎a numerical method is provided for solving multi-term time-fractional diffusion equations associated with a new fractional operator‎. ‎A semi-discrete scheme is obtained in temporal direction based on the finite difference method afterwards‎, ‎a Chebyshev-spectral method is used for spatial discretization‎. ‎Also‎, ‎the stability and error analysis are investigated‎. ‎Moreover‎, ‎the multi-term time-fractional diffusion equation is extended to a distributed order diffusion equation and numerical analysis has been done on it‎. ‎Finally‎, ‎the theoretical results are confirmed using some numerical examples.

کلیدواژه‌ها [English]

• Time fractional diffusion equation
• Spectral Approximation
• Stability analysis
• Error analysis

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### سابقه مقاله

• تاریخ دریافت: 24 دی 1401
• تاریخ بازنگری: 12 اسفند 1401
• تاریخ پذیرش: 16 اردیبهشت 1402
• تاریخ اولین انتشار: 02 خرداد 1402