A Fast Method for Solving the Bagley-Torvik Equation with Time Delay as Delay Differential Equations of Integer Order

Abstract

A method of solving the Bagley-Torvik equation with time delay has been presented in this article, which is based on the physical meaning of that equation and thus avoid the history dependence of it. The most important thing is that the fractional term of the Bagley-Torvik equation is transformed into a solution of a partial differential equation, which is then converted into a set of ordinary differential equations afterwards. An approximation of a boundary condition of the partial differential equations is used as a crucial point. Numerical results have indicated that the computational efficiency has improved significantly. We consider a numerical example with Hopf bifurcation caused by time delay of the Bagley-Torvik equation, which shows that the presented method is computationally more efficient than the predictor-corrector (PC) algorithm with the same time step length.