Computational Mathematics

Comparison of numerical modeling methods for quasi-steady process in conducting nondispersive medium with relaxation

E. A. Bogatyreva

South Ural State University, Chelyabinsk, Russian Federation

Abstract: This article deals with different numerical methods of solving the Dirichlet – Cauchy problem for equation modeling the quasi-steady process in conducting nondispersive medium with relaxation. Known proofs of existence and uniqueness of solution to this problem are not constructive. Therefore the necessity of selection the appropriate numerical method arises. Such method should allow us to find a solution of the considered problem in the reasonable time. The comparative analysis of the Galerkin method and the method of straight lines with $\varepsilon$-embedding method and complex Rosenbrock method is performed in the article. The results of numerical experiments for one-dimensional case are shown.

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

MSC: 65J15

Received: 07.05.2015

Language: English

DOI: 10.14529/jcem150202

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