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Numerical solution of the Bagley-Torvik equation by the Bessel collocation method. (English) Zbl 1261.65081
Summary: 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 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.
MSC:
65L10Boundary value problems for ODE (numerical methods)
34A08Fractional differential equations
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
65L80Numerical methods for differential-algebraic equations
34B05Linear boundary value problems for ODE