یک اسپلاین غیر چند جمله ای برای تقریب معادله بگلی-تورویک کسری

نوع مقاله : مقاله پژوهشی

نویسندگان

گروه ریاضی، دانشکده علوم پایه، دانشگاه رازی، کرمانشاه، ایران

چکیده

در این تحقیق به کمک یک تابع غیر چند جمله ای و عملگر گرانوالد جواب معادله کسری بگلی-توریک را تقریب خواهیم زد. روش های ارائه شده یک سیستم از معادلات را نتیجه می دهد. سپس در ادامه تحلیل خطا برپایه این اسپلاین نمایی و همچنین تحلیل همگرایی روش مورد بحث قرار می گیرد و یک دسته روش از مرتبه دوم بدست می آید. این روش پیشنهادی نه تنها برای حل معادلاتبگلی-ترویک کسری بلکه برای انواع معادلات کسری می تواند مورد استفاده قرار بگیرد. بواسطه مثالهایی کارایی این روش های عددی را با سایر روش های موجود مقایسه می گردد.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

An non-polynomial spline approximation for fractional Bagley-Torvik equation

نویسندگان [English]

  • Sara Ivani
  • Reza Jalilian
Department of Mathematics, Razi University, Kermanshah, Iran
چکیده [English]

In this paper, we approximate the solution of fractional

Bagley–Torvik equation by using the non-polynomial spline function and

the shifted Gr"{u}nwald difference operator. The proposed methods

reduce to the system of algebraic equations. The convergence

analysis of the methods has been discussed. The numerical examples

are presented to illustrate the applications of the methods and to

compare the computed results with the other methods.

کلیدواژه‌ها [English]

  • Caputo derivative
  • Grunwald-Letnikov operator. Non-polynomial spline
  • Convergence analysis
  • Fractional Bagley-Torvik equation
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