Annals of Mathematical Sciences and Applications

Volume 8 (2023)

Number 1

Numerical solution of boundary value problem for the Bagley–Torvik equation using Hermite collocation method

Pages: 157 – 173

DOI: https://dx.doi.org/10.4310/AMSA.2023.v8.n1.a5

Authors

Ayse Gul Kaplan (Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey)

Mulla Veli Ablay (Graduate School of Sciences, Osmaniye Korkut Ata University, Osmaniye, Turkey)

Abstract

In this paper, the boundary value problem of Bagley–Torvik equation, which has an important place in fractional differential equations, is solved using the Hermite collocation method. Various definitions of fractional derivatives have been given in the literature but for boundary value problem, three different types of the mentioned equation were presented to show the accuracy and efficiency of the method. Obtained results were compared with exact solutions and some earlier results. It was seen that the presented method gave very high accuracy numerical results.

Keywords

Hermite polynomials, collocation method, Bagley–Torvik equation, boundary value problem

2010 Mathematics Subject Classification

Primary 33C45, 65L60. Secondary 34A08.

Full Text (PDF format)

Received 7 December 2022

Accepted 20 February 2023

Published 30 March 2023