The behavior of boundary problem solutions is considered for Gred-Shafranov like equation, which describing plasmastatic configurations. It is shown that the application of traditional numerical methods to the problem resolving is shown may lead to significant difficulties, the reason being in the nonuniqueness of the problem solution. The property of nonuniqueness is considered in details (both analytically and numerically) for an assotiated one-dimensional boundary problem with the nonlinearity of the same type. An efficient numerical method is proposed to find all the problem solutions. Basing on developed ideals, the analysis of numerical results for two-dimensional problem is done.

Mathematical modelling in actual problems of science and technics

Petrovskaya N. B.,  KIAM RAS