A highly accurate numerical method for solving boundary value problem of generalized Bagley-Torvik equation

Abstract

A highly accurate numerical method is given for the solution of boundary valueproblem of generalized Bagley-Torvik (BgT) equation with Caputo derivative oforder 0<2 by using the collocation-shooting method (C-SM). The collocation solution is constructed in the space S-m+1((1)) as piecewise polynomials of degreeat most m+1 and has continuous derivative on the considered domain. Furthermore, under some smoothness, conditions of the exact solution convergenceanalysis are given. Numerical investigation is carried on several examples, andbesides showing the justification of theoretical results, comparisons with existing numerical methods are also given. Results indicate that C-SM gives highlyaccurate results and is efficient both in computational time and storage