Solving the First-Order Linear Matrix Differential Equations Using Bernstein Matrix Approach
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
Z. Lorkojouri
1
(Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran)
N. Mikaeilvand
2
(Department of Mathematics, Ardebil Branch, Islamic Azad Unilversity, Ardebil, Iran.)
E. Babolian
3
(Department of Computer Science, Kharazmi University, Tehran, Iran.)
کلید واژه: Operational matrix of derivative, Error estimation., Matrix differential equation, Matrix differential equation, Bernstein polynomials,
چکیده مقاله :
This paper uses a new framework for solving a class of linear matrix differential equations. For doing so, the operational matrix of the derivative based on the shifted Bernstein polynomials together with the collocation method are exploited to decrease the principal problem to system of linear matrix equations. An error estimation of this method is provided. Numerical experiments are reported to show the applicably and efficiency of the propounded method.
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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