Open AccessON NUMERICAL METHODS FOR ONE PROBLEM OF MIXED TYPE
Author(s) -
S. Sytova
Publication year - 2001
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2001.9637171
Subject(s) - mathematics , correctness , type (biology) , convergence (economics) , nonlinear system , constant (computer programming) , numerical analysis , mathematical analysis , computer science , algorithm , ecology , physics , quantum mechanics , economics , biology , programming language , economic growth
This article is devoted to further investigation of numerical methods for one differential problem of mixed type. We consider a two‐dimensional first‐order differential equation with one complex‐valued and one real constant coefficients. So, we have an elliptic problem with respect to the first argument and a hyperbolic problem with respect to the second one. The equations of such type are generalized transfer equations. Firstly, the correctness of the problem stated is discussed. Secondly, possible difference scheme of the multicomponent modification of the alternating direction method is proposed. Its stability and convergence is investigated. Results of numerical experiments on modelling of nonlinear regime of surface volume free electron laser are analyzed.