Geodesic
Computational experiment for one mathematical model of ion-acoustic waves
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 127-132

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In the article the mathematical model of ion-acoustic waves in a plasma in an external magnetic field is studied. This model can be reduced to a Cauchy problem for a Sobolev type equation of the fourth order with polynomially $(A,p)$-bounded operator pencil. Therefore abstract results on solvability of the Cauchy problem for such equation can be used. In the article a theorem on the unique solvability of the Cauchy–Dirichlet problem is mentioned. Based on the theoretical results there was developed an algorithm for the numerical solution of the problem, using a modified Galerkin method. The algorithm is implemented in Maple. The article includes description of this algorithm. It is illustrated by model examples showing the work of the developed program.
Keywords: mathematical model; ion-acoustic waves; Galerkin method. 
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     author = {A. A. Zamyshlyaeva and A. S. Muravyev},
     title = {Computational experiment for one mathematical model of ion-acoustic waves},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
     pages = {127--132},
     publisher = {mathdoc},
     volume = {8},
     number = {2},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a10/}
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A. A. Zamyshlyaeva; A. S. Muravyev. Computational experiment for one mathematical model of ion-acoustic waves. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 8 (2015) no. 2, pp. 127-132. http://geodesic.mathdoc.fr/item/VYURU_2015_8_2_a10/