The numerical solution to the Bagley-Torvik equation by exponential integrators

This paper presents a family of computational schemes for the solution to the Bagley-Torvik equation. The schemes are based on the reformulation of the original problem into a system of fractional dierential equations of order 1/2. Then, suitable exponential integrators are devised to solve the resulting system accurately. The attainable order of convergence of exponential integrators for solving the fractional problem is studied. Theoretical ndings are validated by means of some numerical examples. The advantages of the proposed method are illustrated by comparing several existing methods.