Eur. Phys. J. Plus (2020) 135: 5
https://doi.org/10.1140/epjp/s13360-019-00032-z

Regular Article

Overcoming the near boundary error in the solution of non-homogeneous wave equation by a boundary consistent method

¹ College of Mechanics and Materials, Hohai University, Nanjing, 210098, Jiangsu, China
² Center of Excellence for Ocean Engineering, Center of Excellence for the Oceans, National Taiwan Ocean University, Keelung, 202-24, Taiwan
³ National Engineering Research Center for Intelligent Electrical Vehicle Power System, School of Electromechanical Engineering, Qingdao University, Qingdao, 266071, China

^* e-mail: wfj1218@126.com

Received: 20 January 2019
Accepted: 24 September 2019
Published online: 7 January 2020

Abstract

In the paper, a novel boundary consistent method, modified from the Fourier sine series method, is proposed to solve a non-homogeneous wave equation with non-homogeneous boundary conditions. Besides the usual Fourier sine series, we supplement two extra terms in the solution to consider the consistency of the wave equation at the boundaries. We point out a “mistake” in the conventional Fourier sine series method without considering the boundary consistency conditions, which might cause large boundary errors of the Fourier sine series solution. Numerical examples confirm the improvement of the accuracy of the boundary consistent method, which not only overcomes the boundary errors but also improves the accuracy in the whole domain about four orders, upon comparing with the conventional Fourier sine series method.