NUMERICAL SOLUTIONS FOR NONCLASSICAL EQUATIONS IN THE SPACE OF DIFFERENTIAL FORMS

Abstract

The article contains an overview of results obtained by the author in specially assigned spaces, namely the spaces of differential forms with stochastic coefficients defined on some Riemannian manifold without boundary. This work presents graphs of trajectories of numerical solutions to the Cauchy problem for the Barenblatt--Zheltov--Kochina equation and the Showalter--Sidorov problem for the Dzektser and Ginzburg--Landau equations. Since the equations are studied in a space of differential forms, the operators themselves are understood in a special form, in particular, instead of the Laplace operator, we take its generalization that is the Laplace--Beltrami operator. Graphs of coefficients of differential forms obtained during the computational experiments are given for different values of the parameters of the initial equations.