On the convergence of difference schemes of high accuracy for the equation of ion-acoustic waves in a magnetized plasma

Abstract

Multiparametric difference schemes of the finite element method of a high order of accuracy for the Sobolevtype equation of the fourth-order in time are studied. In particular, the first boundary value problem for the equation of ion-acoustic waves in a magnetized plasma is considered. A high-order accuracy of the scheme is achieved due to the special discretization of time and space variables. The presence of parameters in the scheme makes it possible to regularize the accuracy of the schemes and optimize the implementation algorithm. An a priori estimate in a weak norm is obtained by the method of energy inequality. Based on this estimate and the Bramble-Hilbert lemma, the convergence of the constructed algorithms in classes of generalized solutions is proved. An algorithm for implementing the difference scheme is proposed.