Numerical solution of the Bagley-Torvik equation by the Bessel collocation method

YÜZBAŞI Ş.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, cilt.36, sa.3, ss.300-312, 2013 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 3
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1002/mma.2588
  • Dergi Adı: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.300-312
  • Anahtar Kelimeler: Bagley-Torvik equation, fractional differential equations, Caputo fractional derivative, Bessel collocation method, Bessel functions of the first kind, FRACTIONAL DIFFERENTIAL-EQUATIONS, INTEGRODIFFERENTIAL EQUATIONS, RESIDUAL CORRECTION, SYSTEMS, CALCULUS, ORDER
  • Akdeniz Üniversitesi Adresli: Evet

Özet

In this article, a numerical technique is presented for the approximate solution of the BagleyTorvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the BagleyTorvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples. Copyright (c) 2012 John Wiley & Sons, Ltd.

In this article, a numerical technique is presented for the approximate solution of the Bagley–Torvik equation, which is a class of fractional differential equations. The basic idea of this method is to obtain the approximate solution in a generalized form of the Bessel functions of the first kind. For this purpose, by using the collocation points, the matrix operations and a generalization of the Bessel functions of the first kind, this technique transforms the Bagley–Torvik equation into a system of the linear algebraic equations. Hence, by solving this system, the unknown Bessel coefficients are computed. The reliability and efficiency of the proposed scheme are demonstrated by some numerical examples.