Geodesic
On numerical solution in the space of differential forms for one stochastic Sobolev-type equation with a relatively radial operator
Journal of computational and engineering mathematics, Tome 7 (2020) no. 4, pp. 48-55

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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. 
@article{JCEM_2020_7_4_a4,
     author = {D. E. Shafranov},
     title = {On numerical solution in the space of differential forms for one stochastic {Sobolev-type} equation with a relatively radial operator},
     journal = {Journal of computational and engineering mathematics},
     pages = {48--55},
     publisher = {mathdoc},
     volume = {7},
     number = {4},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JCEM_2020_7_4_a4/}
}
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D. E. Shafranov. On numerical solution in the space of differential forms for one stochastic Sobolev-type equation with a relatively radial operator. Journal of computational and engineering mathematics, Tome 7 (2020) no. 4, pp. 48-55. http://geodesic.mathdoc.fr/item/JCEM_2020_7_4_a4/