On the numerical solution of Bagley-Torvik equation via the Laplace transform

Abstract

In this work, we formulate a numerical scheme for the solution of the Bagley-Torvik equation using an integral representation in complex plane. The resultant integral is approximated to high order accuracy using quadrature. The accuracy of numerical algorithm depends on the selection of optimal contour of integration. Several contour have been developed in the literature for solving FDEs. In the present work, we will investigate the applicability of optimal contours for solving Bagley-Torvik equation. We compared our results with other methods available in the literature to validate the efficiency and accuracy of the method for various optimal contour of integrations.