On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients

Wim T. van Horssen, Yandong Wang, Guohua Cao

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)

Abstract

In this paper, it is shown how characteristic coordinates, or equivalently how the well-known formula of d'Alembert, can be used to solve initial-boundary value problems for wave equations on fixed, bounded intervals involving Robin type of boundary conditions with time-dependent coefficients. A Robin boundary condition is a condition that specifies a linear combination of the dependent variable and its first order space-derivative on a boundary of the interval. Analytical methods, such as the method of separation of variables (SOV) or the Laplace transform method, are not applicable to those types of problems. The obtained analytical results by applying the proposed method, are in complete agreement with those obtained by using the numerical, finite difference method. For problems with time-independent coefficients in the Robin boundary condition(s), the results of the proposed method also completely agree with those as for instance obtained by the method of separation of variables, or by the finite difference method.

Original languageEnglish
Pages (from-to)263-271
Number of pages9
JournalJournal of Sound and Vibration
Volume424
DOIs
Publication statusPublished - 2018

Keywords

  • Characteristic coordinates
  • Formula of d'Alembert
  • Robin boundary condition
  • Time-dependent coefficient
  • Wave equation

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