### ON NUMERICAL SOLUTION IN THE SPACE OF DIFFERENTIAL FORMS FOR ONE STOCHASTIC SOBOLEV-TYPE EQUATION WITH A RELATIVELY RADIAL OPERATOR

#### Abstract

The paper presents graphs of the trajectories of numerical solutions to the Showalter -- Sidorov problem for one stochastic version of the Ginzburg -- Landau equation in spaces of differential forms defined on a two-dimensional torus. We use the previously obtained transition from the deterministic version of the theory of Sobolev type equations to stochastic equations using the Nelson -- Glicklikh derivative. Since the equations are studied in the space of differential forms, the operators themselves are understood in a special form, in particular, instead of the Laplace operator, we take its generalization, the Laplace -- Beltrami operator. The graphs of computational experiments are given for different values of the parameters of the initial equation for the same trajectories of the stochastic process.

#### Keywords

Sobolev type equation; white noise; Nelson -- Gliklikh derivative; Riemannian manifold; differential forms; Laplace -- Beltrami operator; numerical solution.

#### Full Text:

PDF### Refbacks

- There are currently no refbacks.