Volume 8, no. 2Pages 127 - 132 # Computational Experiment for One Mathematical Model of Ion-acoustic Waves

A.A. Zamyshlyaeva, A.S. MuravyevIn 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.

Full text- 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)