Print Email Facebook Twitter On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients Title On solving wave equations on fixed bounded intervals involving Robin boundary conditions with time-dependent coefficients Author van Horssen, W.T. (TU Delft Mathematical Physics) Wang, Y. (TU Delft Mathematical Physics; China University of Mining and Technology) Cao, G. (China University of Mining and Technology) Date 2018 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. Subject Characteristic coordinatesFormula of d'AlembertRobin boundary conditionTime-dependent coefficientWave equation To reference this document use: http://resolver.tudelft.nl/uuid:0d475332-5377-45d3-8dc6-212ff990cd58 DOI https://doi.org/10.1016/j.jsv.2018.03.009 Embargo date 2022-02-25 ISSN 0022-460X Source Journal of Sound and Vibration, 424, 263-271 Bibliographical note Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project https://www.openaccess.nl/en/you-share-we-take-care Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public. Part of collection Institutional Repository Document type journal article Rights © 2018 W.T. van Horssen, Y. Wang, G. Cao Files PDF 1_s2.0_S0022460X1830186X_main.pdf 1.23 MB Close viewer /islandora/object/uuid:0d475332-5377-45d3-8dc6-212ff990cd58/datastream/OBJ/view