This article is cited in 3 papers

Computational Mathematics

Numerical modeling of quasi-steady process in conducting nondispersive medium with relaxation

E. A. Bogatyreva

South Ural State University, Chelyabinsk, Russian Federation

Abstract: Sufficient conditions of existence and uniqueness of weak generalized solution to the Dirichlet – Cauchy problem for equation modeling a quasi-steady process in conducting nondispersive medium with relaxation are obtained. The main equation of the model is considered as a representative of the class of quasi-linear equations of Sobolev type. It enables to prove a solvability of the Dirichlet – Cauchy problem in a weak generalized meaning by methods developed for this class of equations. In suitable functional spaces the Dirichlet – Cauchy problem is reduced to the Cauchy problem for abstract quasi-linear operator differential equation of the special form. Algorithm of numerical solution to the Dirichlet – Cauchy problem based on the Galerkin method is developed. Results of computational experiment are provided.

Keywords: Galerkin method, quasi-linear Sobolev type equation, weak generalized solution, numerical modeling.

MSC: 65J15

Received: 24.02.2015

Language: English

DOI: 10.14529/jcem150105

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