An Efficient and Accurate Hybrid Method for 1-D Wave Problem with Non-Classical Boundary Conditions

Valmir BAME; Lulezim HANELLI

doi:10.21276/ijirem.2020.7.1.1

Abstract

A new numerical method is proposed for the solution of 1-D initial-boundary value wave problem with non-classical boundary conditions. It combines the finite difference method with that of characteristics. The second method operates near the boundary of integration domain and it implements accurately the non-classical boundary conditions. Meantime, the difference method operates efficiently and accurately in the interior of the domain. The key element is the achieving of a satisfying balance between accuracy and efficiency. The method is implemented and tested in Matlab.

Keywords

Initial-boundary value problem, Hyperbolic differential equation, Damping conditions, Difference methods, Characteristics, Conventional order, Accuracy-efficiency balance.

Reference

[1] Bame, V. and Hanelli, L. 2019. Numerical solution for semi linear hyperbolic differential equations. InternationalJournal of Innovative Research in Engineering & Management (IJIREM), Volume-6, Issue-4, July 2019. DOI= https://DOI: 10.21276/ijirem.2019.6.4.1

[2] Cox, S. and Zuazua, E. 1995. The rate at which energy decays in a string damped at one end. Indiana University Mathematics Journal 44, 1995, 545-573.

[3] Darmawijoyo and van Horssen, W. T. 2003. On the weakly damped vibrations of a string attached to a spring-massdashpot system. J.Vib. Control. 9, (2003), pp. 1231-1248.

[4] Darmawijoyo, van Horssen W. T. and Clement Ph. 2003. On a Rayleigh wave equation with boundary damping. Nonlinear Dyn. 33, (2003), pp. 399-429.

[5] Huti, B. and Hanelli, L. (2016). Numerical solution for a wave equation arising in oscillations of overhead transmission lines. International Journal of Innovation in Science and Mathematics [Online]. http://ijism.org/administrator/components/com_jresearch/fil e s/publications/IJISM_533_Final.pdf

[6] Tyn Myint-U, T. and Debnath, L. 2007. Linear partial differential equations for scientists and engineers. Birkhauser Boston, New York.

[7] Wang, H., Elcrat, A. R., and Egbert, R. I. 1993. Modeling and boundary control of conductor galloping. J. Sound Vib. 161, (1993), 301-315.

Cites this article as

V. BAME, L. H. , "An Efficient and Accurate Hybrid Method for 1-D Wave Problem with Non-Classical Boundary Conditions", International Journal of Innovative Research in Engineering & Management (IJIREM), Vol-7, Issue-1, Page No-1-5, 2020. Available from: https://doi.org/10.21276/ijirem.2020.7.1.1