Geodesic
Numerical solutions for the Cauchy problem for the Oskolkov equation in the spaces of differential forms with stochastic coefficients
Journal of computational and engineering mathematics, Tome 10 (2023) no. 2, pp. 42-51.

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The article contains a research of the solvability of the Cauchy problem for the linear Oskolkov equation in specially given spaces, namely the spaces of differential forms with stochastic coefficients defined on some Riemannian manifold without boundary. This work presents graphs of coefficients of differential forms that are solutions to the Cauchy problem for Oskolkov equations. Since the equations are studied in 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 within other computational experiments are presented for various values of parameters of the Oskolkov equation.
Keywords: Sobolev type equation, differential forms, Riemannian manifold, Laplace – Beltrami operator, numerical solution. 
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     author = {D. E. Shafranov},
     title = {Numerical solutions for the {Cauchy} problem for the {Oskolkov} equation in the spaces of differential forms with stochastic coefficients},
     journal = {Journal of computational and engineering mathematics},
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     url = {http://geodesic.mathdoc.fr/item/JCEM_2023_10_2_a3/}
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D. E. Shafranov. Numerical solutions for the Cauchy problem for the Oskolkov equation in the spaces of differential forms with stochastic coefficients. Journal of computational and engineering mathematics, Tome 10 (2023) no. 2, pp. 42-51. http://geodesic.mathdoc.fr/item/JCEM_2023_10_2_a3/