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Zbl 1188.65107
Çenesiz, Yücel; Keskin, Y ild iray; Kurnaz, Ayd in
The solution of the Bagley-Torvik equation with the generalized Taylor collocation method. (English)
[J] J. Franklin Inst. 347, No. 2, 452-466 (2010). ISSN 0016-0032; ISSN 1879-2693/e

Summary: The Bagley-Torvik equation, which has an important role in fractional calculus, is solved by generalizing the Taylor collocation method [cf. {\it R. L. Bagley} and {\it P. J. Torvik} [J. Appl. Mech. 51, 294--298 (1984; Zbl 1203.74022)]. The proposed method has a new algorithm for solving fractional differential equations. This new method has many advantages over variety of numerical approximations for solving fractional differential equations. To assess the effectiveness and preciseness of the method, results are compared with other numerical approaches. Since the Bagley-Torvik equation represents a general form of the fractional problems, its solution can give many ideas about the solution of similar problems in fractional differential equations.

MSC 2000:: *65L60 Finite numerical methods for ODE
34A08
65L05 Initial value problems for ODE (numerical methods)

Keywords: Bagley-Torvik equation; generalized Taylor collocation method; Adomian decomposition method; differential transform method; numerical examples; fractional calculus; algorithm; fractional differential equations

Citations: Zbl 1203.74022

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