Numerical Solution of a SIR Fractional Model of the Distribution of Computer Viruses Using Dickson Polynomials
محورهای موضوعی : مجله بین المللی ریاضیات صنعتیD. Shirani 1 , M. Tavassoli ‎Kajani‎ 2 , S. Salahshour 3
1 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
2 - Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, Iran.
3 - Department of Mathematics, Mobarakeh Branch, Islamic Azad University, Isfahan, Iran.
کلید واژه: Dickson polynomials, Fractional model of computer virus, Collocation method,
چکیده مقاله :
In this paper, a numerical method is presented using a Dickson-based collocations method to solve a fractional model of computer virus propagation. The model presented in this paper is a system of differential equations of fraction. By using the Dickson-based collocation method and using Chebyshev's spatial points, we transform the system of deficit differential equations into a system of algebraic equations. In this way, an approximate solution can be found for the proposed model. By introducing the error functions for the expressed fractional model, the accuracy and convergence of the obtained solutions are investigated. Some of the approximate results obtained using this method is displayed in the numerical results section.
در این مقاله یک روش عددی با استفاده از روش کالوکیشن(هم مکانی) برپایه چند جمله ایهای دیکسون برای حل یک مدل کسری از انتشار ویروسهای کامپیوتری ارائه شده است. مدل ارائه شده در این مقاله یک دستگاه معادلات دیفرانسیل کسری است. با بکاربردن روش کالوکیشن برپایه چندجمله ایهای دیکسون و استفاده از نقاط هم مکانی چبیشف دستگاه معادلات دیفرانسیل کسری را به یک دستگاه معادلات جبری تبدیل می کنیم. به این ترتیب یافتن یک جواب تقریبی برای مدل ارائه شده میسر می گردد. با معرفی تابع خطا برای مدل کسری بیان شده، دقت و همگرایی جواب های بدست آمده، مورد بررسی قرار می گیرد. برخی از جوابهای تقریبی بدست آمده با استفاده از این روش، در قسمت نتایج عددی نمایش داده می شوند.
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