文章基本信息

标题：On the solution of an acoustic wave equation with variable-order derivative loss operator
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作者：Abdon Atangana
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2013
卷号：2013
期号：1
页码：167
DOI：10.1186/1687-1847-2013-167
语种：English
出版社：Hindawi Publishing Corporation
摘要：When modeling sound propagation, the use of fractional derivatives leads to models that better describe observations of attenuation and dispersion. The wave equation for viscous losses involving integer-order derivatives only leads to an attenuation which is proportional to the square of the frequency. This does not always reflect reality. The acoustic wave equation with loss operator is generalized to the concept of variable-order derivatives in this work. The generalized equation is solved via the Crank-Nicholson scheme. The stability and the convergence of this case are examined in detail.
关键词：acoustic wave equation ; loss operator ; variable-order derivative ; Crank-Nicholson scheme ; stability ; convergence