Volume 8, no. 2Pages 127 - 132

Computational Experiment for One Mathematical Model of Ion-acoustic Waves

A.A. Zamyshlyaeva, A.S. Muravyev
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.
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Keywords
mathematical model; ion-acoustic waves; Galerkin method.
References
1. Zamyshlyaeva A.A. Lineynye uravneniya sobolevskogo tipa vysokogo poryadka [Linear Sobolev Type Equations of High Order]. Chelyabinsk, Publ. Center of the South Ural State University, 2012.
2. Sveshnikov A.G., Al'shin A.B., Korpusov M.O., Pletner Yu.D. Lineynye i nelineynye uravneniya sobolevskogo tipa [Linear and Non-Linear Equations of Sobolev Type]. Moscow, FIZMATLIT, 2007.
3. Zamyshlyaeva A.A. [Stochastic Mathematical Model of Ion-Acoustic Waves in a Plasma]. Estestvennye i tekhnicheskie nauki [Natural and Technical Sciences], 2013, no. 4, pp. 284-292. (in Russian)
4. Zamyshlyaeva A.A. [A Mathematical Model of Ion-Acoustic Waves in a Plasma in a Magnetic Field]. Materialy mezhdunarodnoy konferentsii 'Voronezhskaya zimnyaya matematicheskaya shkola S.G. Kreyna - 2014', 2014, pp. 142-144. (in Russian)