حل معادلات دیفرانسیل ماتریسی خطی مرتبه اول با استفاده از رویکرد ماتریس برنشتاین

Subject Areas : International Journal of Industrial Mathematics

زهرا لرکوجوری ¹ , ناصر میکائیل وند ² , اسماعیل بابلیان ³

1 - گروه ریاضی، واحد علوم و تحقیقات، دانشگاه آزاد اسلامی، تهران، ایران.
2 - گروه ریاضی، واحد اردبیل، دانشگاه آزاد اسلامی، اردبیل، ایران.
3 - گروه علوم ریاضی و کامپیوتر، دانشگاه خوارزمی، تهران، ایران.

Received: 2020-03-23 Accepted : 2020-05-17 Published : 2021-04-01

Keywords: چند جمله‌ایی های برنشتاین, ماتریس عملگر مشتق, معادله دیفرانسیل ماتریسی, تحلیل خطا,

Abstract :

در این مقاله از یک چارچوب جدید برای حل یک رده از معادلات دیفرانسیل ماتریسی خطی استفاده شده است. برای انجام این کار، ماتریس عملیاتی مشتق مبتنی بر چند جمله ای برنشتاین انتقال یافته همراه با روش همبستگی برای کاهش مسئله اصلی به دستگاه معادلات ماتریس خطی مورد بهره برداری قرار می گیرد. تخمین خطای این روش ارائه شده است. آزمایش­های عددی برای نمایش کاربرد و کارایی روش ارائه شده است.

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